Chaos, fractional kinetics, and anomalous transport

Physics Report

Volumn 371, Issue 6, 2002, Pages 461-580

  Zaslavsky, G M ^a,b  

^a NEW YORK UNIVERSITY   (United States)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Anomalous transport; Chaos; Fractional kinetics

Indexed keywords

EID: 0036887936     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(02)00331-9     Document Type: Review

References (307)

1. Abdullaev, S.S., 2000. Phys. Rev. E 62, 3508.
2. Abdullaev, S.S., Eich, Th., Finken, K.H., 2001. Phys. Plasmas 8, 2739.
3. Abdullaev, S.S., Finken, K.H., Kaleck, A., Spatchek, K.H., 1998. Phys. Plasmas 5, 196.
4. Abdullaev, S.S., Spatchek, K.H., 1999. Phys. Rev. E 60, R6287.
5. Abdullaev, S.S., Zaslavsky, G.M., 1996. Phys. Plasmas 3, 516.
6. Afanasiev, V.V., Sagdeev, R.Z., Zaslavsky, G.M., 1991. Chaos 1, 143.
7. Afraimovich, V., 1997. Chaos 7, 12.
8. Afraimovich, V., Zaslavsky, G.M., 1997. Phys. Rev. E 55, 5418.
9. Afraimovich, V., Zaslavsky, G.M., 1998. In: Benkadda, S., Zaslavsky, G.M. (Eds.), Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas. Springer, Berlin.
10. Agullo, O., Verga, A.D., Zaslavsky, G.M., 1997. Phys. Rev. E 55, 5587.
11. Aizawa, Y., Kikuchi, Y., Harayama, T., Yamamoto, K., Ota, M., Tanaka, K., 1989. Prog. Theor. Phys. Suppl. 98, 36.
12. Annibaldi, S.V., Manfredi, G., Dendy, R.O., Drury, L.O'C., 2000. Plasma Phys. Control. Fusion 42, L13.
13. Aquino, G., Grigolini, P., Scafetta, N., 2001. Chaos Solitons Fractals 12, 2023.
14. Aranson, I.S., Rabinovich, M.I., Tsimring, L.Sh., 1990. Phys. Lett. A 151, 523.
15. Aref, H., Pomphrey, N., 1980. Phys. Lett. A 78, 297.
16. Aref, H., Pomphrey, N., 1982. Proc. R. Soc. London A 380, 359.
17. Aref, H., 1984. J. Fluid Mech. 143, 1.
18. Arnold, V.I., 1965. C.R. Acad. Sci. Paris 261, 17.
19. Arnold, V.I., 1978. Mathematical Methods of Classical Mechanics. Springer, Berlin.
20. Artale, V., Boffetta, G., Celani, A., Cencini, M., Vulpiani, A., 1997. Phys. Fluids 9, 3162.
21. Artuso, R., Guarneri, I., Rebuzzini, L., 2000. Chaos 10, 189.
22. Artuso, R., Casati, G., Guarneri, I., 1997. Phys. Rev. E 55, 6384.
23. Artuso, R., Prampolini, 1998. Phys. Lett. A 246, 407.
24. Artuso, R., Rusconi, M., 2001. Phys. Rev. E 64, 015204.
25. Ashwin, P., Chambers, W., Petkov, F., 1997. Int. J. Bifurcations Chaos 7, 2603.
26. Aurell, E., Boffetta, G., Crisanti, A., Paladin, G., Vulpiani, A., 1997. J. Phys. A 30, 1.
27. Babiano, A., Boffetta, G., Provenzale, A., Vulpiani, A., 1994. Phys. Fluids 6, 2465.
28. Badii, R., Politi, A., 1997. Complexity. Cambridge University Press, Cambridge.
29. Bagchi, B., Zwanzig, R., Marchetti, M., 1985. Phys. Rev. A 31, 892.
30. Balescu, R., 1997. Phys. Rev. E 55, 2465.
31. Baptista, M.S., Caldas, I.L., 2000. Physica A 284, 348.
32. Baptista, M.S., Caldas, I.L., Heller, M.V.A.P., Ferreira, A.A., 2001. Physica A 301, 150.
33. Barkai, E., 2001. Phys. Rev. E 63, 046118.
34. Beloshapkin, V.V., Chernikov, A.A., Natenzon, M.Ya., Petrovichev, B.A., Sagdeev, R.Z., Zaslavsky, G.M., 1989. Nature 337, 113.
35. Benenti, G., Casati, G., Montangero, S., Shepelyansky, D., 2001. Phys. Rev. Lett. 87, 227901.
36. Benkadda, S., Gabbai, P., Zaslavsky, G.M., 1997a. Phys. Plasmas 4, 2864.
37. Benkadda, S., Kassibrakis, S., White, R.B., Zaslavsky, G.M., 1997b. Phys. Rev. E 55, 4909.
38. Benkadda, S., Kassibrakis, S., White, R.B., Zaslavsky, G.M., 1999. Phys. Rev. E 59, 3761.
39. Berger, J.M., Mandelbrot, B.B., 1963. IBM J. Res. Dev. 7, 224.
40. Beyer, P., Benkadda, S., 2001. Chaos 11, 774.
41. Biler, P., Funaki, T., Woyczynski, W.A., 1998. J. Differential Equations 148, 9.
42. Boatto, S., Pierrehumbert, R.T., 1999. J. Fluid Mech. 394, 137.
43. Bohr, T., Jensen, M.H., Paladin, G., Vulpiani, A., 1998. Dynamical Systems Approach to Turbulence. Cambridge University Press, Cambridge, MA.
44. Bonci, L., Grigolini, P., Laux, A., Roncaglia, R., 1996. Phys. Rev. A 54, 112.
45. Bouchaud, J.P., Georges, A., 1990. Phys. Rep. 95, 127.
46. Bowen, R., 1972. Am. J. Math. 94, 413.
47. Bunimovich, L.A., Sinai, Ya.G., 1973. Math. USSR-Sb. 90, 407.
48. Bunimovich, L.A., Sinai, Ya.G., 1981. Commun. Math. Phys. 78, 479.
49. Butzer, P.L., Westphal, U., 2000. In: Hilfer, R. (Ed.), Applications of Fractional Calculus in Physics. World Scientific, Singapore.
50. Cardoso, O., Tabeling, P., 1988. Europhys. Lett. 7, 225.
51. Carreras, B.A., Lynch, V.E., Newman, D.E., Zaslavsky, G.M., 1999. Phys. Rev. E 60, 4770.
52. Carreras, B.A., Lynch, V.E., Zaslavsky, G.M., 2001. Phys. Plasmas 8, 5096.
53. Casati, G., Prosen, T., 1999. Phys. Rev. Lett. 83, 4729.
54. Castiglioni, P., Mazzino, A., Muratore-Gnanneschi, P., Vulpiani, A., 1999. Physica D 134, 75.
55. Chaikovsky, D.K., Zaslavsky, G.M., 1991. Chaos 1, 463.
56. Chechkin, A.V., Gonchar, V.Yu., 2000. Chaos Solitons Fractals 11, 2379.
57. Chechkin, A.V., Gonchar, V.Yu., Szydlowski, M., 2002. Phys. Plasmas 9, 78.
58. Chernikov, A.A., Petrovichev, B.A., Rogalsky, A., Sagdeev, R.Z., Zaslavsky, G.M., 1990. Phys. Lett. A 144, 127.
59. Chernov, N., Young, L.-S., 2000, preprint.
60. Chirikov, B.V., 1979. Phys. Rep. 52, 263.
61. Chirikov, B.V., Shepelyansky, D.L., 1984. Physica D 13, 395.
62. Chua, L.O., Lin, T., 1998. IEEE Trans. 35, 648.
63. Chukbar, K.V., 1995. JETP 81, 1025.
64. Cizeau, P., Bouchaud, J.P., 1994. Phys. Rev. E 50, 1810.
65. Compte, A., 1996. Phys. Rev. E 53, 4191.
66. Cornfeld, I.P., Fomin, S.V., Sinai, Ya.G., 1982. Ergodic Theory. Springer, New York.
67. Crisanti, A., Falcioni, M., Provenzale, A., Tanga, P., Vulpiani, A., 1992. Phys. Fluids A 4, 1805.
68. del-Castillo-Negrette, D., Morrison, P.J., 1993. Phys. Fluids A 5, 948.
69. Denisov, S., Flach, S., 2001. Phys. Rev. E 64, 056236.
70. Dorfman, J.R., 1999. An Introduction to Chaos in Nonequilibrium Statistical Mechanics. Cambridge University Press, Cambridge, MA.
71. Douglas, J.F., 2000. In: Hilfer, R. (Ed.), Applications of Fractional Calculus in Physics. World Scientific, Singapore, pp. 241.
72. Douglas, J.F., Wang, S.-Q., Freed, K.F., 1986. Macromolecules 19, 2207.
73. Douglas, J.F., Wang, S.-Q., Freed, K.F., 1987. Macromolecules 20, 543.
74. Feller, W., 1949. Trans. Am. Math. Soc. 67, 98.
75. Feller, W., 1957. An Introduction to Probability Theory and Its Applications. Wiley, New York.
76. Ferrari, R., Manfroi, A.J., Young, W.R., 2001. Physica D 154, 111.
77. Feynman, R.P., Hibbs, A.R., 1965. Quantum Mechanics and Path Integrals. McGraw-Hill, New York.
78. Flach, S., Yevtushenko, O., Zolotaryuk, Y., 2000. Phys. Rev. Lett. 84, 2358.
79. Fogedby, H.C., 1994. Phys. Rev. E 50, 1657.
80. Fokker, A.D., 1914. Ann. Phys. 43, 812.
81. Fox, C., 1961. Trans. Am. Math. Soc. 98, 395.
82. Galperin, G.A., Zemlyakov, A.N., 1990. Mathematical Billiards. Nauka, Moscow (in Russian).
83. Geisel, T., 1984. Europhys. News 15, 5.
84. Geisel, T., 1995. In: Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (Eds.), Lévy Flights and Related Topics in Physics. Springer, Berlin, pp. 153.
85. Geisel, T., Nierwetberg, J., 1984. Phys. Rev. Lett. 29, 2305.
86. Geisel, T., Nierwetberg, J., Zacherl, A., 1987a. Phys. Rev. Lett. 54, 616.
87. Geisel, T., Zacherl, A., Radons, G., 1987b. Phys. Rev. Lett. 59, 2503.
88. Gelfand, I.M., Shilov, G.E., 1964. Generalized Functions, Vol. 1. Academic, New York.
89. Gnedenko, B.V., Kolmogorov, A.N., 1954. Limit Distributions for Sums of Independent Variables. Addison-Wesley, Cambridge, MA.
90. Gorenflo, R., De Fabritiis, G., Mainardi, F., 1999. Physica A 269, 79.
91. Grassberger, P., Procaccia, I., 1984. Physica D 13, 34.
92. Greene, J.M., 1979. J. Math. Phys. 20, 1183.
93. Greene, J.M., MacKay, R.S., Vivaldi, F., Feigenbaum, M.J., 1981. Physica D 3, 468.
94. Gutkin, E., 1986. Physica D 19, 311.
95. Gutkin, E., 1996. J. Stat. Phys. 83, 7.
96. Haake, F., 2001. Quantum Signatures of Chaos. Springer, Berlin.
97. Haller, G., 2000. Chaos 10, 99.
98. Haller, G., 2001a. Physica D 149, 248.
99. Haller, G., 2001b. Chaos 11, 431.
100. Halsey, T.C., Jensen, M.H., Kadanoff, L.P., Procaccia, I., Schraiman, B.I., 1986. Phys. Rev. A 33, 1141.
101. Hannay, J.H., McCraw, R.J., 1990. J. Phys. A 23, 887.
102. Hanson, J.D., Cary, J.R., Meiss, J.D., 1985. J. Stat. Phys. 39, 327.
103. Henon, M., 1966. C.R. Acad. Sci. Paris 262, 312.
104. Hentschel, H.G.E., Procaccia, I., 1983. Physica D 8, 435.
105. Hilfer, R., 1993. Phys. Rev. E 48, 2466.
106. Hilfer, R., 1995a. Chaos Solitons Fractals 5, 1475.
107. Hilfer, R., 1995b. Physica A 221, 89.
108. Hilber, R., 2000. In: Hilfer, R. (Ed.), Application of Fractional Calculus in Physics. World Scientific, Singapore, pp. 429.
109. Hohenberg, P.C., Halperin, B.I., 1977. Rev. Mod. Phys. 49, 435.
110. Horton, W., 1981. Plasma Phys. 23, 1107.
111. Hughes, B.D., Montroll, E.W., Shlesinger, M.F., 1982. J. Stat. Phys. 28, 111.
112. Hughes, B.D., Shlesinger, M.F., Montroll, E.W., 1981. Proc. Natl. Acad. Sci. USA 78, 3287.
113. Ichikawa, Y.H., Kamimura, T., Hatori, T., 1987. Physica D 29, 247.
114. Iomin, A., Zaslavsky, G.M., 1999. Phys. Rev. E 60, 7580.
115. Iomin, A., Zaslavsky, G.M., 2000. Chaos 10, 147.
116. Iomin, A., Zaslavsky, G.M., 2001. Phys. Rev. E 63, 047203.
117. Iomin, A., Zaslavsky, G.M., 2002. Not published.
118. Iomin, A., Gangardt, D., Fishman, S., 1998. Phys. Rev. E 57, 4054.
119. Ishizaki, R., Horito, T., Kobayashi, T., Mori, M., 1991. Prog. Theor. Phys. 85, 1013.
120. Isichenko, M.B., 1992. Rev. Mod. Phys. 64, 961.
121. Ivanov, P.Ch., Podobnik, B, Lee, Y., Stanley, H.E., 2001. Physica A 229, 154.
122. Jensen, M.H., Kadanoff, L.P., Libshaber, A., Procaccia, I., Stavans, J., 1985. Phys. Rev. Lett. 55, 439.
123. Jones, S.W., Young, W.R., 1994. J. Fluid Mech. 280, 149.
124. Kac, M., 1958. Probability and Related Topics in Physical Sciences. Interscience, New York.
125. Kadanoff, L.P., 1981. Phys. Rev. Lett. 47, 1641.
126. Kadanoff, L.P., 1993. From Order to Chaos. World Scientific, Singapore.
127. Kadanoff, L.P., 2000. Statistical Physics. World Scientific, Singapore.
128. Kaplan, A., Friedman, N., Andersen, M., Davidson, N., 2001. Phys. Rev. Lett. 87, 274101.
129. Karney, C.F.F., 1983. Physica D 8, 360.
130. Kassibrakis, S., Benkadda, S., White, R.B., Zaslavsky, G.M., 1998. In: Benkadda, S., Zaslavsky, G.M. (Eds.), Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas. Springer, Berlin, pp. 403.
131. Katok, A., 1987. Commun. Math. Phys. 111, 151.
132. Khinchin, A.Ya., 1964. Continued Fractions. University of Chicago Press, Chicago, IL.
133. Klafter, J., Blumen, A., Shlesinger, M.F., 1987. Phys. Rev. A 35, 3081.
134. Klafter, J., Zumofen, G., 1994. Phys. Rev. E 49, 4873.
135. Kleva, R.G., Drake, J.F., 1984. Phys. Fluids 27, 1686.
136. Kolmogorov, A.N., 1938. Usp. Mat. Nauk 5, 5.
137. Kouptsov, K.L., Lowenstein, J.H., Vivaldi, F., 2002, Preprint.
138. Kovalyov, S., 2000. Chaos 10, 153.
139. Kuznetsov, L., Zaslavsky, G.M., 1998. Phys. Rev. E 58, 7330.
140. Kuznetsov, L., Zaslavsky, G.M., 2000. Phys. Rev. E 61, 3777.
141. Kusnezov, D., 1994. Phys. Rev. Lett. 72, 1990.
142. Kusnezov, D., Bulgac, A., Dang, G., 1999. Phys. Rev. Lett. 82, 1136.
143. Kusnezov, D., Lewenkopf, C.H., 1996. Phys. Rev. E 53, 2283.
144. Laforgia, A., Leoncini, X., Kuznetsov, L., Zaslavsky, G.M., 2001. Eur. Phys. J. B 20, 427.
145. Lamb, H., 1945. Hydrodynamics. Dover, New York.
146. Landau, L.D., 1937. Zh. Eksp. Teor. Fiz. 7, 203.
147. Landau, L.D., Lifshits, E.M., 1976. Mechanics. Pergamon Press, Oxford.
148. Laskin, N., 2000a. Phys. Rev. E 62, 3135.
149. Laskin, N., 2000b. Phys. Lett. A 268, 298.
150. Latora, V., Rapisarda, A., Ruffo, S., 2000. Physica A 280, 81.
151. Leboeuf, P., 1998. Physica D 116, 8.
152. Leff, H.S., Rex, A.F. (Eds.), 1990. Maxwell's Demon. Princeton University Press, Princeton, NJ.
153. Leoncini, X., Zaslavsky, G.M., 2002. Phys. Rev. E 165, 046216.
154. Leoncini, X., Kuznetsov, L., Zaslavsky, G.M., 2001. Phys. Rev. E 63, 036224.
155. Lepri, S., Rondoni, L., Benettin, G., 2000. J. Stat. Phys. 99, 857.
156. Lesnik, D., Spatschek, K.H., 2001. Phys. Rev. E 64, 056205.
157. Lévy, P., 1937. Theorie de L'Addition des Variables Aleatoires. Gauthier-Villars, Paris.
158. Lichtenberg, A., Lieberman, M., 1983. Regular and Chaotic Motion. Springer, Berlin.
159. Lowenstein, J.H., Vivaldi, F., 1998. Nonlinearity 11, 1321.
160. Lowenstein, J.H., Hatjispyros, S., Vivaldi, F., 1997. Chaos 7, 49.
161. Lutz, E., 2001. Phys. Rev. Lett. 86, 2208.
162. Machta, J., 1983. J. Stat. Phys. 32, 555.
163. Machta, J., Zwanzig, R., 1983. Phys. Rev. Lett. 48, 1959.
164. MacKay, R.S., 1983. Physica D 7, 283.
165. MacKay, R.S., Meiss, J.D., Percival, I.C., 1984. Physica D 13, 55.
166. Mainardi, F., 1996a. Chaos Solitons Fractals 7, 1461.
167. Mainardi, F., 1996b. Appl. Math. Lett. 9, 23.
168. Mainardi, F., 1997. In: Carpinteri, A., Mainardi, F. (Eds.), Fractals and Fractional Calculus in Continuum Mechanics. Springer, New York, pp. 291.
169. Majda, A.J., Kramer, P.R., 1999. Phys. Rep. 314, 238.
170. Mandelbrot, B., 1982. The Fractal Geometry of Nature. Freeman, San Francisco.
171. Mandelbrot, B., Van Ness, J.W., 1968. SIAM Rev. 10, 422.
172. Margulis, G.A., 1969. Funkts. Anal. i Prilozh. 3, 80.
173. Margulis, G.A., 1970. Funkts. Anal. i Prilozh. 4, 62.
174. Marksteiner, S., Ellinger, K., Zoller, P., 1996. Phys. Rev. A 53, 3409.
175. Mateos, J.L., 2000. Phys. Rev. Lett. 84, 258.
176. Meerschaert, M.M., ScheZer, H.P., 2000. Limit Theorems for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. Wiley, New York.
177. Meerschaert, M.M., Benson, D.A., Baeumer, B., 2001. Phys. Rev. E 63, 021112.
178. Meiss, J.D., 1986. Phys. Rev. A 34, 2375.
179. Meiss, J.D., 1992. Rev. Mod. Phys. 64, 795.
180. Meiss, J.D., 1997. Chaos 7, 39.
181. Meiss, J.D., Ott, E., 1985. Phys. Rev. Lett. 55, 2741.
182. Meiss, J.D., Ott, E., 1986. Physica D 20, 387.
183. Meiss, J.D., Cary, J.R., Grebogi, C., Crawford, J.D., Kaufman, A.N., Abarbanel, H.D., 1983. Physica D 6, 375.
184. Meleshko, V.V., 1994. Phys. Fluids 6, 6.
185. Meleshko, V.V., Konstantinov, M.Yu., 2002. Vortex Dynamics Chaotic Phenomena. World Scientific, Singapore.
186. Melnikov, V.K., 1996. in: Benkadda, S.S., Doveil, F., Elskens, Y. (Eds.), Transport, Chaos, and Plasma Physics 2, Vol. 142. World Scientific, Singapore.
187. Metzler, R., Klafter, J., 2000. Phys. Rep. 339, 1.
188. Miller, K.S., Ross, B., 1993. An Introduction to the Fractional Differential Equations. Wiley, New York.
189. Milovanov, A.V., 2001. Phys. Rev. E 63, 047301.
190. Milovanov, A.V., Zelenyi, L.M., 2001. Phys. Rev. E 64, 052101.
191. Montroll, E.W., Scher, H., 1973. J. Stat. Phys. 9, 101.
192. Montroll, E.W., Shlesinger, M.F., 1984. in: Lebowitz, J., Montroll, E. (Eds.), Studies in Statistical Mechanics, Vol. 11. North-Holland, Amsterdam, p. 1.
193. Montroll, E.W., Weiss, G.H., 1965. J. Math. Phys. 6, 167.
194. Morozov, A.I., Soloviev, L.S., 1966. In: Leontovich, M.A. (Ed.), Review of Plasma Physics, Vol. 2. Consultants Bureau, NY, p. 1.
195. Naulin, V., Nielsen, A.H., Rasmussen, J.J., 1999. Phys. Plasmas 6, 4575.
196. Neishtadt, A.I., Chaikovsky, D.K., Chernikov, A.A., 1991. Zb. Eksp. Teor. Fiz. 99, 763.
197. Neufeld, Z., Tel, T., 1997. J. Phys. A 30, 2263.
198. Newhouse, S., 1977. Am. J. Math. 99, 1061.
199. Nezlin, M.V., 1994. Chaos 4, 187.
200. Niemeijer, Th., van Leeuwen, J.M.J., 1976. in: Domb, C., Green, M.S. (Eds.), Phase Transitions and Critical Phenomena, Vol. 6. Academic Press, London, p. 425.
201. Nigmatullin, 1986. Phys. Stat. Solidi B 133, 425.
202. Novikov, E.A., 1975. JETP 41, 937.
203. Ott, E., 1993. Chaos in Dynamical Systems. Cambridge University Press, Cambridge, MA.
204. Ottino, J., 1989. The Kinematics of Mixing: Stretching, Chaos, Transport. Cambridge University Press, Cambridge, MA.
205. Paladin, G., Vulpiani, A., 1987. Phys. Rep. 156, 147.
206. Panoiu, N., 2000. Chaos 10, 166.
207. Parisi, G., Frisch, U., 1985. In: Ghil, M., Benzi, R., Parisi, G. (Eds.), Turbulence and Predictability of Geophysical Flows and Climate Dynamics. North-Holland, Amsterdam, pp. 71.
208. Pedlosky, J., 1987. Geophysical Fluid Dynamics. Springer, Berlin.
209. Percival, I.C., 1980. In: Herrera, J.C. (Ed.), Nonlinear Dynamics and the Beam-Beam Interaction. AIP, New York, pp. 302.
210. Petrovichev, B.A., Rogalsky, A.V., Sagdeev, R.Z., Zaslavsky, G.M., 1990. Phys. Lett. 150, 391.
211. Planck, M., 1917. Sitzungsber Preuss. Akad. Wiss., 324.
212. Provenzale, A., 1999. Annu. Rev. Fluid Mech. 31, 55.
213. Ragot, B.R., Kirk, J.G., 1997. Astron. Astrophys. 327, 432.
214. Rakhlin, D.A., 2000. Phys. Rev. E 63, 011112-1.
215. Rechester, A.B., White, R.B., 1980. Phys. Rev. Lett. 44, 1586.
216. Rechester, A.B., Rosenbluth, M.N., White, R.B., 1981. Phys. Rev. A 23, 2664.
217. Risken, H., 1989. The Fokker-Planck Equation: Methods of Solution and Applications. Springer, Berlin.
218. Rom-Kedar, V., 1994. Nonlinearity 7, 441.
219. Rom-Kedar, V., Zaslavsky, G.M., 1999. Chaos 9, 697.
220. Rom-Kedar, V., Leonard, A., Wiggins, S., 1990. J. Fluid Mech. 214, 347.
221. Roncaglia, R., Bonci, L., West, B.J., Grigolini, P., 1995. Phys. Rev. E 51, 5524.
222. Sagdeev, R.Z., Usikov, D.A., Zaslavsky, G.M., 1988. Nonlinear Physics: From the Pendulum to Turbulence and Chaos. Harwood, New York.
223. Saichev, A.I., Woyczynski, W.A., 1997. Distributions in the Physical and Engineering Sciences, Vol. 1. Birkhäuser, Boston.
224. Saichev, A.I., Zaslavsky, G.M., 1997. Chaos 7, 753.
225. Samko, S.G., Kilbas, A.A., Marichev, O.I., 1987. Fractional Integrals and Derivatives and Their Applications. Nauka i Tekhnika, Minsk (Translation by Harwood, Schur, 1993).
226. Sapoval, B., Gobron, Th., Margolina, A., 1991. Phys. Rev. Lett. 67, 2974.
227. Scher, M., Shlesinger, M.F., Bendler, J.T., 1991. Phys. Today 1, 26.
228. Schertzer, D., Larcheveque, M., Duan, J., Yanovsky, V.V., Lovejoy, S., 2001. J. Math. Phys. 42, 200.
229. Schneider, W.R., Wyss, W., 1989. J. Math. Phys. 30, 134.
230. Schwägerl, M., Krug, J., 1991. Physica D 52, 143.
231. Shlesinger, M.F., 1988. Annu. Rev. Phys. Chem. 39, 269.
232. Shlesinger, M.F., 1989. Physica D 38, 304.
233. Shlesinger, M.F., Hughes, B.D., 1981. Physica A 109, 597.
234. Shlesinger, M.F., Klafter, J., 1989. J. Phys. Chem. 93, 7023.
235. Shlesinger, M.F., Klafter, J., Zumofen, G., 1995a. Fractals 3, 491.
236. Shlesinger, M.F., West, B.J., 1991. Phys. Rev. Lett. 67, 2106.
237. Shlesinger, M.F., West, B.J., Klafter, J., 1987. Phys. Rev. Lett. 58, 1100.
238. Shlesinger, M.F., Zaslavsky, G.M., Frisch, U., 1995b. (Eds.), Lévy Flights and Related Topics in Physics. Springer, Berlin.
239. Shlesinger, M.F., Zaslavsky, G.M., Klafter, J., 1993. Nature 363, 31.
240. Sholl, D.S., Skodje, R.T., 1994. Physica D 71, 168.
241. Sinai, Ya.G., 1963. Dokl. Akad. Nauk SSSR 153, 1261. [Sov. Math. 4, 1818].
242. Solomon, T.H., Fogleman, M.A., 2001. Physica D 157, 40.
243. Solomon, T.H., Gollub, J., 1988. Phys. Rev. A 38, 6280.
244. Solomon, T.H., Weeks, E.R., Swinney, H.L., 1993. Phys. Rev. Lett. 71, 3975.
245. Solomon, T.H., Weeks, E.R., Swinney, H.L., 1994. Physica D 76, 70.
246. Sommeria, J., Meyers, S.D., Swinney, H.L., 1989. Nature 337, 58.
247. Sornette, D., 1998. Phys. Rep. 297, 239.
248. Stefancich, M., Allegrini, P., Bonci, L., Grigolini, P., West, B.J., 1998. Phys. Rev. E 57, 6625.
249. Sundaram, B., Zaslavsky, G.M., 1999. Phys. Rev. E 59, 7231.
250. Uchaikin, V.V., 1998. Physica A 255, 65.
251. Uchaikin, V.V., 1999. JETP 88, 1155.
252. Uchaikin, V.V., 2000. J. Theor. Phys. 39, 2087.
253. Uchaikin, V.V., Zolotarev, V.M., 1999. Chance and Stability. VSP, Utrecht.
254. Venkatarami, S.C., Antonsen Jr., T.M., Ott, E., 1997. Phys. Rev. Lett. 78, 3864.
255. Vivaldi, F., 1994. Eksperimental Math. 3, 303.
256. Vlad, M., Spineanu, F., Misguich, J.H., Balescu, R., 1998. Phys. Rev. E 58, 7359.
257. Weeks, E.R., Urbach, J.S., Swinney, H.L., 1996. Physica D 97, 291.
258. Weiss, G.H., 1994. Aspects and Applications of the Random Walk. North-Holland, Amsterdam.
259. Weiss, J., Knobloch, E., 1989. Phys. Rev. A 40, 2579.
260. Weiss, J.B., Provenzale, A., McWilliams, J.C., 1998. Phys. Fluids 10, 1929.
261. Weitzner, H., Zaslavsky, G.M., 2001. Chaos 11, 384.
262. West, B., 2000. J. Phys. Chem. B 104, 3830.
263. West, B.J., Grigolini, P., 2000. In: Hilfer, R. (Ed.), Applications of Fractional Calculus in Physics. World Scientific, Singapore, pp. 171.
264. West, B.J., Grigolini, P., Metzler, R., Nonnenmacher, T.F., 1997. Phys. Rev. E 55, 99.
265. White, R.B., Benkadda, S., Kassibrakis, S., Zaslavsky, G.M., 1998. Chaos 8, 757.
266. Wiersig, J., 2000. Phys. Rev. E 62, R21. 8.
267. Wiggins, S., 1992. Chaotic Transport in Dynamical Systems. Springer, Berlin.
268. Wilson, K., Kogut, J., 1974. Phys. Rep. 12, 75.
269. Wyss, W., 1986. J. Math. Phys. 27, 2782.
270. Yanovsky, V.V., Chechkin, A.V., Schertzer, D., Tur, A.V., 2000. Physica A 282, 13.
271. Young, L.-S., 1999. Isr. J. Math. 110, 153.
272. Young, W., Jones, S., 1990. Phys. Fluids A 3, 1087.
273. Young, W., Pumir, A., Pomeau, Y., 1989. Phys. Fluids A 1, 462.
274. Zacherl, A., Geisel, T., Nierwetberg, J., 1986. Phys. Lett. 114A, 317.
275. Zanetti, L., Franzese, P., 1993. Eur. J. Mech. B 12, 43.
276. Zaslavsky, G.M., 1981. Phys. Rep. 80, 157.
277. Zaslavsky, G.M., 1985. Chaos in Dynamic Systems. Harwood, Amsterdam.
278. Zaslavsky, G.M., 1992. In: Moffatt, H.K., Zaslavsky, G.M., Comte, P., Tabor, M. (Eds.), Topological Aspects of the Dynamics of Fluids and Plasmas. Kluwer, Dordrecht, pp. 481.
279. Zaslavsky, G.M., 1994a. Physica D 76, 110.
280. Zaslavsky, G.M., 1994b. Chaos 4, 25.
281. Zaslavsky, G.M., 1995. Chaos 5, 653.
282. Zaslavsky, G.M., 1999. Phys. Today 8, 39.
283. Zaslavsky, G.M., 2000a. In: Hilfer, R. (Ed.), Application of Fractional Calculus in Physics. World Scientific, Singapore, pp. 203.
284. Zaslavsky, G.M., 2000b. Physica A 288, 431.
285. Zaslavsky, G.M., 2002. Physica D 168-169, 292.
286. Zaslavsky, G.M., Abdullaev, S.S., 1995. Phys. Rev. E 51, 3901.
287. Zaslavsky, G.M., Edelman, M., 1997. Phys. Rev. E 56, 5310.
288. Zaslavsky, G.M., Edelman, M., 2000. Chaos 10, 135.
289. Zaslavsky, G.M., Edelman, M., 2001. Chaos 11, 295.
290. Zaslavsky, G.M., Edelman, M., 2002. Not published.
291. Zaslavsky, G.M., Edelman, M., Niyazov, B., 1997. Chaos 7, 159.
292. Zaslavsky, G.M., Edelman, M., Weitzner, H., Carreras, B., McKee, G., Bravenec, R., Fonck, R., 2000. Phys. Plasmas 7, 3691.
293. Zaslavsky, G.M., Filonenko, N.N., 1968. Sov. Phys. JETP 25, 851.
294. Zaslavsky, G.M., Niyazov, B., 1997. Phys. Rep. 283, 73.
295. Zaslavsky, G.M., Sagdeev, R.Z., Chaikovsky, D.K., Chernikov, A.A., 1989a. JETP 68, 995.
296. Zaslavsky, G.M., Sagdeev, R.Z., Chernikov, A.A., 1988. JETP 67, 270.
297. Zaslavsky, G.M., Sagdeev, R.Z., Usikov, D.A., Chernikov, A.A., 1991. Weak Chaos and Quasi-regular Patterns. Cambridge University Press, Cambridge.
298. Zaslavsky, G.M., Stevens, D., Weitzner, H., 1993. Phys. Rev. E 48, 1683.
299. Zaslavsky, G.M., Tippett, M.K., 1991. Phys. Rev. Lett. 67, 3251.
300. Zaslavsky, G.M., Zakharov, M.Yu., Neishtadt, A.I., Sagdeev, R.Z., Usikov, D.A., Chernikov, A.A., 1989b. JETP 69, 885.
301. Zaslavsky, G.M., Zakharov, M.Yu., Sagdeev, R.Z., Usikov, D.A., Chernikov, A.A., 1986. Sov. Phys. JETP 64, 294.
302. Ziglin, S.L., 1982. Physica D 4, 268.
303. Zimbardo, G., Greco, A., Vetri, P., 2000a. Phys. Plasmas 7, 1071.
304. Zimbardo, G., Veltri, P., Pommois, P., 2000b. Phys. Rev. E 61, 1940.
305. Zolotarev, V.M., Uchaikin, V.V., Saenko, V.V., 1999. JETP 88, 780.
306. Zorich, A., 1997. Ergodic Theory Dyn. Sys. 17, 1477.
307. Zwanzig, R., 1983. J. Stat. Phys. 30, 255.