Dynamical entropy for systems with stochastic perturbation

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 2, 2000, Pages 2018-2029

  Ostruszka, Andrzej ^a   Pakoński, Prot ^a   Słomczyński, Wojciech ^a   Życzkowski, Karol ^a,b  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY; RANDOM PROCESSES; SPECTRUM ANALYSIS; SPURIOUS SIGNAL NOISE;

BOLTZMANN-GIBBS ENTROPY; DETERMINISTIC SYSTEM; FROBENIUS-PERRON OPERATOR; KOLMOGOROV-SINAI ENTROPY; LOGISTIC MAP; RANDOM ADDITIVE NOISE; TRIGONOMETRIC NOISE;

DYNAMICS;

EID: 0034238980     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.2018     Document Type: Article

References (59)

1. G. Paladin, M. Serva, and A. Vulpiani, Phys. Rev. Lett. 74, 66 (1995).
2. V. Loreto, G. Paladin, M. Pasquini, and A. Vulpiani, Physica A 232, 189 (1996).
3. A. Namenson, E. Ott, and T. M. Antonsen, Phys. Rev. E 53, 2287 (1996).
4. V. Loreto, G. Paladin, and A. Vulpiani, Phys. Rev. E 53, 2087 (1996).
5. J. P. Crutchfield, D. J. Farmer, and B. A. Huberman, Phys. Rep. 92, 45 (1982).
6. J. M. Deutsch, J. Phys. A 18, 1457 (1985).
7. K. Matsumoto and I. Tsuda, J. Phys. A 18, 3561 (1985).
8. T. Kapitaniak, Chaos in Systems with Noise (World Scientific, Singapore, 1988).
9. A. R. Bulsara, E. W. Jacobs, and W. C. Schieve, Phys. Rev. A 42, 4614 (1990).
10. L. Yu, E. Ott, and Q. Chen, Phys. Rev. Lett. 65, 2935 (1990).
11. P. Cvitanović, C. P. Dettmann, R. Mainieri, and G. Vattay, J. Stat. Phys. 93, 981 (1998).
12. Yu. Kifer, Izv. Acad. Nauk SSSR Mat. 38, 1091 (1974) [Izv. Acad. Sci. USSR, Math 8, 1083 (1974)].
13. M. Boyarsky, Trans. Am. Math. Soc. 257, 350 (1980).
14. L.-S. Young, Erg. Theor. Dyn. Sys. 6, 311 (1986).
15. Y. Kifer, Random Perturbation of Dynamical Systems (Birkhäuser, Boston, 1988).
16. V. Baladi and L.-S. Young, Commun. Math. Phys. 156, 355 (1993).
17. A. Lasota and M. C. Mackey, Chaos, Fractals and Noise (Springer-Verlag, New York, 1994).
18. M. Blank, Discreteness and Continuity in Problems of Chaotic Dynamics (American Mathematical Society, Providence, RI, 1997).
19. M. Blank and G. Keller, Nonlinearity 10, 81 (1997).
20. A. Boyarsky and P. Góra, Laws of Chaos (Birkhäuser, Boston, 1997).
21. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic Theory (Springer-Verlag, Berlin, 1982).
22. W. Słomczyński and K. Życzkowski, J. Math. Phys. 35, 5674 (1994).
23. J. Kwapień, W. Słomczyński, and K. Życzkowski, J. Phys. A 30, 3175 (1997).
24. W. Słomczyński and K. Życzkowski, Phys. Rev. Lett. 80, 1880 (1998).
25. A. Ostruszka, Master thesis, Kraków, 1997 (unpublished).
26. S. Guiaşu, Information Theory with Applications (McGraw-Hill, New York, 1977).
27. N. F. G. Martin and J. W. England, Mathematical Theory of Entropy (Addison-Wesley, Reading, MA, 1981).
28. G. Jumarie, Relative Information (Springer-Verlag, Berlin, 1990).
29. J. N. Kapur, Measures of Information and Their Applications (John Wiley & Sons, New York, 1994).
30. J. P. Crutchfield and N. H. Packard, Physica D 7, 201 (1983).
31. P. Gaspard and X.-J. Wang, Phys. Rep. 235, 291 (1993).
32. A. Cohen and I. Procaccia, Phys. Rev. A 31, 1872 (1985).
33. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
34. R. F. Fox, Chaos 5, 619 (1995).
35. G. Casati and B. Chirikov, in Quantum Chaos. Between Order and Disorder, edited by G. Casati and B. Chirikov (Cambridge University Press, Cambridge, 1995).
36. A. V. Andreev, B. D. Simons, O. Agam, and B. L. Altshuler, Nucl. Phys. B 482, 536 (1996).
37. A. Wehrl, Rep. Math. Phys. 16, 353 (1979).
38. P. Szépfalusy and G. Györgyi, Phys. Rev. A 33, 2852 (1986).
39. M. Misiurewicz and K. Ziemian, in Proceedings of the Conference on Ergodic Theory and Related Topics II, Georgenthal, 1986, edited by H. Michel (Teubner, Leipzig, 1987), pp. 147–159.
40. K. Życzkowski and W. Słomczyński, Phys. Rev. E 52, 6879 (1995).
41. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, Products (Academic, New York, 1965).
42. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
43. P. Gaspard, J. Stat. Phys. 68, 673 (1992).
44. I. Antoniou and S. Tasaki, Physica A 190, 303 (1992).
45. H. H. Hasegawa and W. C. Saphir, Phys. Rev. A 46, 7401 (1992).
46. P. Gaspard, Chaos 3, 427 (1993).
47. H. H. Hasegawa and D. J. Driebe, Phys. Rev. E 50, 1781 (1994).
48. R. F. Fox, Chaos 7, 254 (1997).
49. G. Keller, Commun. Math. Phys. 96, 181 (1984).
50. M. Blank and G. Keller, Nonlinearity 11, 1351 (1998).
51. M. F. Barnsley, Fractals Everywhere, 2nd ed. (Academic, Boston, 1993).
52. W. Słomczyński, Chaos, Solitons and Fractals 8, 1861 (1997).
53. W. Słomczyński (unpublished).
54. W. Słomczyński, J. Kwapień, and K. Życzkowski, Chaos 10, 180 (2000).
55. T. Kaijser, Rev. Roum. Math. Pures Appl. 26, 1075 (1981).
56. J. H. Elton, Ergod. Theor. Dynam. Sys. 7, 481 (1987).
57. F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991).
58. J. Weber, F. Haake, and P. Šeba, LANL Report No. nlin.CD/0001013, 2000.
59. S. Fishmann, in Supersymmetry and Trace Formulae, edited by I. V. Lerner, J. P. Keating, and D. E. Khmelnitskii, NATO Advanced Study Insitute, Series B: Physics Vol. 370 (Kluwer Academic/Plenum Publishers, New York, 1999).