Finite size Lyapunov exponent: Review on applications

Journal of Physics A: Mathematical and Theoretical

Volumn 46, Issue 25, 2013, Pages

  Cencini, Massimo ^a   Vulpiani, Angelo ^a,b  

^a ISC CNR   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84878858516     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/46/25/254019     Document Type: Review

References (117)

1. Oseledec V I 1968 Trans. Moscow Math. Soc. 19 197
2. Kolmogorov A N 1958 Dokl. Akad. Nauk SSSR 119 861
3. Sinai Y G 1959 Dokl. Akad. Nauk SSSR 124 768
4. Lorenz E N 1969 Tellus 21 289
5. Lorenz E 1995 The Essence of Chaos (Seattle: University of Washington Press)
6. Aurell E, Boffetta G, Crisanti A, Paladin G and Vulpiani A 1996 Phys. Rev. Lett. 77 1262
7. Dressler U and Farmer J D 1992 Physica D 59 365
8. Torcini A, Grassberger P and Politi A 1995 J. Phys. A: Math. Gen. 28 4533
9. Letz T and Kantz H 2000 Phys. Rev. E 61 2533
10. Kolmogorov A N 1956 IRE Trans. Inform. Theor. IT-2 102
11. Kolmogorov A N and Tikhomirov V M 1959 Usp. Math. Nauk 14 3
12. Boffetta G, Paladin G and Vulpiani A 1996 J. Phys. A: Math. Gen. 29 2291 (Pubitemid 126069656)
13. Aurell E, Boffetta G, Crisanti A, Paladin G and Vulpiani A 1997 J. Phys. A: Math. Gen. 30 1 (Pubitemid 127011902)
14. Boffetta G, Celani A, Cencini M, Lacorata G and Vulpiani A 2000 Chaos 10 50
15. Lacorata G, Aurell E, Legras B and Vulpiani A 2004 J. Atmos. Sci. 61 2936 (Pubitemid 40098855)
16. Gaspard P and Wang X J 1993 Phys. Rep. 235 291
17. Shannon C E 1948 Bell Syst. Tech. J. 27 379
18. Shannon C E 1948 Bell Syst. Tech. J. 27 623
19. Billingsley P 1965 Ergodic Theory and Information (New York: Wiley)
20. Eckmann J P and Ruelle D 1985 Rev. Mod. Phys. 57 617
21. Pesin Y B 1977 Russ. Math. Surv. 32 55
22. Abel M, Biferale L, Cencini M, Falcioni M, Vergni D and Vulpiani A 2000 Physica D 147 12 (Pubitemid 33592755)
23. Cencini M, Falcioni M, Kantz H, Olbrich E and Vulpiani A 2000 Phys Rev. E 62 427
24. Palmer T 1996 Predictability of the atmosphere and oceans: from days to decades Decadal Climate Variability: Dynamics and Predictability (NATO ASI Series vol 144) (Berlin: Springer) p 83
25. Lorenz E N 1996 Predictability - a problem partly solved Predictability: ECMWF Seminar Proc. (4-5 Sept. 1995) (Reading: ECMWF) p 1
26. Herrera S, Pazó D, Fernández J and Rodríguez M 2011 Tellus A 63 978
27. Boffetta G, Giuliani P, Paladin G and Vulpiani A 1998 J. Atmos. Sci. 55 3409
28. Olbrich E, Hegger R and Kantz H 1998 Phys. Lett. A 244 538
29. Grassberger P and Procaccia I 1983 Phys. Rev. Lett. 50 346
30. Boffetta G, Celani A, Cencini M, Lacorata G and Vulpiani A 2000 J. Phys. A: Math. Gen. 33 1313
31. Palmer T 2001 Quart. J. R. Meteor. Soc. 127 279
32. Peña M and Kalnay E 2004 Nonlinear Process. Geophys. 11 319
33. Toth Z and Kalnay E 1997 Mon. Weather Rev. 125 3297
34. Kalnay E 2002 Atmospheric Modeling, Data Assimilation and Predictability (Cambridge: Cambridge University Press)
35. Toth A and Kalnay E 1993 Bull. Am. Meteorol. Soc. 74 2317
36. Yoden S 2007 J. Meteorol. Soc. Japan B 85 77
37. Boffetta G, Cencini M, Falcioni M and Vulpiani A 2002 Phys. Rep. 356 367
38. Boffetta G, Mazzino A and Vulpiani A 2008 J. Phys. A: Math. Theor. 41 363001
39. Frisch U 1995 Turbulence: The Legacy of A N Kolmogorov (Cambridge: Cambridge University Press)
40. Leith C E 1971 J. Atmos. Sci. 28 144
41. Leith C E and Kraichnan R H 1972 J. Atmos. Sci. 29 1041
42. Ruelle D 1979 Phys. Lett. A 72 81
43. Crisanti A, Jensen M H, Paladin G and Vulpiani A 1993 Phys. Rev. Lett. 70 166 (Pubitemid 23684133)
44. Biferale L 2003 Annu. Rev. Fluid Mech. 35 441 (Pubitemid 37515242)
45. Boffetta G and Ecke R 2012 Annu. Rev. Fluid Mech. 44 427
46. Boffetta G and Musacchio S 2000 Phys. Fluids A 13 1060
47. Basu S, Foufoula-Georgiou E and Porté-Agel F 2002 Geophys. Res. Lett. 29 2038
48. Chaté H and Manneville P 1992 Prog. Theor. Phys. 87 1
49. Perez G and Cerdeira H A 1992 Phys. Rev. A 46 7492
50. Pikovsky A S and Kurths J 1994 Phys. Rev. Lett. 72 1644
51. Kaneko K 1995 Physica D 86 158
52. Chaté H and Manneville P 1996 Physica A 224 348
53. Losson J, Vannitsem S and Nicolis G 1998 Phys. Rev. E 57 4921
54. Shibata T and Kaneko K 1998 Phys. Rev. Lett. 81 4116
55. Cencini M, Falcioni M, Vergni D and Vulpiani A 1999 Physica D 130 58
56. Takeuchi K, Ginelli F and Chaté H 2009 Phys. Rev. Lett. 103 154103
57. Olmi S, Politi A and Torcini A 2010 Europhys. Lett. 92 60007
58. Nicolis C and Nicolis G 1984 Nature 311 529
59. Osborne A R and Provenzale A 1989 Physica D 35 357
60. Sugihara G and May R 1990 Nature 344 734
61. Casdagli M J 1991 J. R. Stat. Soc. B 54 303
62. Kaplan D T and Glass L 1992 Phys. Rev. Lett. 68 427
63. Kubin G 1995 What is a chaotic signal? IEEE Workshop on Nonlinear Signal and Image Processing (Halkidiki, Greece,) p 141
64. Olbrich E and Kantz H 1997 Phys. Lett. A 232 63
65. Gao J B, Hu J, Tung W W and Cao Y H 2006 Phys. Rev. E 74 066204 (Pubitemid 44936013)
66. Abarbanel H D I 1996 Analysis of Observed Chaotic Data (New York: Springer-Verlag)
67. Kantz H and Schreiber T 1997 Nonlinear Time Series Analysis (Cambridge: Cambridge University Press)
68. Gelfand I M, Kolmogorov A N and Yaglom A M 1958 Amount of information and entropy for continuous distributions Selected Works of A N Kolmogorov vol 3 ed A N Shiryeyev (Dordrecht: Kluwer) p 33
69. Grassberger P and Procaccia I 1983 Physica D 9 189
70. Schell M, Fraser S and Kapral R 1982 Phys. Rev. A 26 504
71. Crutchfield J P and Kaneko K 1988 Phys. Rev. Lett. 60 2715
72. Politi A, Livi R, Oppo G L and Kapral R 1993 Europhys. Lett. 22 571
73. Ginelli F, Livi R and Politi A 2002 J. Phys. A: Math. Gen. 35 499 (Pubitemid 37024006)
74. Politi A and Torcini A 2010 Stable chaos Nonlinear Dynamics and Chaos: Advances and Perspectives ed M Thiel (Berlin: Springer) p 103
75. Politi A and Torcini A 1994 Europhys. Lett. 28 545
76. Cencini M and Torcini A 2001 Phys. Rev. E 63 056201
77. Bagnoli F and Cecconi F 2000 Phys. Lett. A 282 9
78. Baroni L, Livi R and Torcini A 2001 Phys. Rev. E 63 036226
79. Ahlers V and Pikovsky A 2002 Phys. Rev. Lett. 88 254101
80. Ginelli F, Livi R, Politi A and Torcini A 2003 Phys. Rev. E 67 046217
81. Ginelli F, Cencini M and Torcini A 2009 J. Stat. Mech. 2009 P12018
82. Vega J L, Uzer T and Ford J 1993 Phys. Rev. E 48 3414
83. Mantica G 2000 Phys. Rev. E 61 6434
84. Chirikov B and Vivaldi F 1999 Physica D 129 223
85. Gutkin E 1996 J. Stat. Phys. 83 7
86. Cecconi F, del Castillo-Negrete D, Falcioni M and Vulpiani A 2003 Physica D 180 129
87. Jepps O G and Rondoni L 2006 J. Phys. A: Math. Gen. 39 1311 (Pubitemid 43146205)
88. Benettin G, Galgani L, Giorgilli A and Strelcyn J M 1980 Meccanica 15 9
89. Mitchell L and Gottwald G 2012 Chaos 22 023115
90. Zillmer R, Livi R, Politi A and Torcini A 2006 Phys. Rev. E 74 036203 (Pubitemid 44343487)
91. Sawford B 2001 Annu. Rev. Fluid Mech. 33 289-317 (Pubitemid 32573220)
92. Salazar J and Collins L 2009 Annu. Rev. Fluid Mech. 41 405-32
93. Ottino J M 1990 Annu. Rev. Fluid Mech. 22 207
94. Crisanti A, Falcioni M, Paladin G and Vulpiani A 1991 Riv. Nuovo Cimento 14 1
95. Artale V, Boffetta G, Celani A, Cencini M and Vulpiani A 1997 Phys. Fluids 9 3162
96. Boffetta G, Cencini M, Espa S and Querzoli G 2000 Phys. Fluids 12 3160 (Pubitemid 32015469)
97. Jullien M 2003 Phys. Fluids 15 2228 (Pubitemid 37096642)
98. Lacorata G, Aurell E and Vulpiani A 2001 Ann. Geophys. 19 121
99. Richardson L F 1926 Proc. R. Soc. Lond. A 110 709
100. Biferale L, Boffetta G, Celani A, Devenish B, Lanotte A and Toschi F 2005 Phys. Fluids 17 115101 (Pubitemid 43045739)
101. Boffetta G, Celani A, Crisanti A and Vulpiani A 1999 Europhys. Lett. 46 177
102. Boffetta G and Sokolov I M 2002 Phys. Rev. Lett. 88 094501
103. Piterbarg L I 2012 Appl. Math. Model. 36 3464
104. Batchelor G 1952 Math. Proc. Camb. Phil. Soc. 48 345
105. Morel P and Larceveque M 1974 J. Atmos. Sci. 31 2189
106. Joseph B and Legras B 2002 J. Atmos. Sci. 59 1198
107. Koh T and Legras B 2002 Chaos 12 382
108. d'Ovidio F, Fernández V, Hernández-García E and López C 2004 Geophys. Res. Lett. 31 17203 (Pubitemid 39583632)
109. d'Ovidio F, Isern-Fontanet J, López C, Hernández- García E and García-Ladona E 2009 Deep-Sea Res. I 56 15
110. Hernández-Carrasco I, López C, Hernández- García E and Turiel A 2011 Ocean Modelling 36 208
111. Rossi V, López C, Sudre J, Hernández-García E and Garçon V 2008 Geophys. Res. Lett. 35 L11602
112. Tew Kai E, Rossi V, Sudre J, Weimerskirch H, López C, Hernández-García E, Marsac F and Garçon V 2009 Proc. Natl Acad. Sci. USA 106 8245
113. d'Ovidio F, Monte S D, Alvain S, Dandonneau Y and Lévy M 2010 Proc. Natl Acad. Sci. USA 107 18366
114. Haller G 2001 Phys. Fluids 13 3365 (Pubitemid 33066938)
115. Haller G and Yuan G 2000 Physica D 147 352
116. Haller G and Beron-Vera F 2012 Physica D 241 1680
117. Cencini M, Cecconi F and Vulpiani A 2009 Chaos: From Simple Models to Complex Systems (Singapore: World Scientific)