Dynamical systems and computable information

Discrete and Continuous Dynamical Systems - Series B

Volumn 4, Issue 4, 2004, Pages 935-960

  Benci, V ^a   Bonanno, C ^a   Galatolo, S ^a   Menconi, G ^a   Virgilio, M ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Data compression; Information; Weak chaos

Indexed keywords

EID: 4944246972     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2004.4.935     Document Type: Article

References (35)

1. Aaronson J., "An introduction to infinite ergodic theory", American Mathematical Society, 1997
2. Argenti F., Benci V., Cerrai P., Cordelli A., Galatolo S., Menconi G., Information and dynamical systems: a concrete measurement on sporadic dynamics, Chaos, Solitons and Fractals, 13 (2002), no. 3, 461-469
3. Arnold V.I., Avez A., "Ergodic problems of classical mechanics", Benjamin, 1968
4. Bell T., Witten I. H., Cleary J. G., Modeling for text compression, ACM Computing Surveys, 21 (1989), 557-591
5. Benci V., Galatolo S., Optimal information measures for weakly chaotic dynamical systems, submitted to proceedings of General Theory of Information Transfer and Combinatorics, Bielefeld 2002
6. Bonanno C., "Applications of information measures to chaotic dynamical systems", Ph.D. dissertation, University of Pisa, 2003
7. Bonanno C, Galatolo S, Algorithmic information for intermittent systems with an indifferent fixed point, http://arxiv.org/abs/math.DS/0403070
8. Bonanno C, Galatolo S, Isola S, Recurrence and algorithmic information, Nonlinearity, 17 (2004), 1057-1074
9. Bonanno C., Menconi G., Computational information for the logistic map at the chaos threshold, Disc. Cont. Dyn. Syst.- B, 2 (2002), no.3, 415-431
10. Brudno A.A., Entropy and the complexity of the trajectories of a dynamical system, Trans. Moscow Math. Soc., 2 (1983), 127-151
11. Campanino M., Isola S.,Infinite invariant measures for non-uniformly expanding transformations of [0,1]: weak law of large numbers with anomalous scaling, Forum Math., 8 (1996), 71-92
12. Casati G., Prosen T., Triangle map: a model of quantum chaos, Phys. Rev. Lett., 88 (2000), 4261-4264
13. Chaitin G. J., "Information, randomness and incompleteness, papers on algorithmic information theory", World Scientific, Singapore, 1987
14. Cohen A., Procaccia I., Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems, Phys. Rev. A, 31 (1985), 1872-1882
15. Collet P., Eckmann J.-P., "Iterated maps on the interval as dynamical systems", Birkhauser, 1980
16. Collet P., Ferrero P., Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point, Ann. Inst. H. Poincarè, 52 (1990), 283-301.
17. Feigenbaum M. J., Quantitative universality for a class of nonlinear transformations, J. Stat. Phys., 19 (1978), no. 1, 25-52
18. Feller W., Fluctuation theory of recurrent events, Trans. Amer. Math. Soc., 67 (1949), 98-119
19. Froeschlé C., A Numerical Study of the Stochasticity of Dynamical Systems with two Degrees of Freedom, Astron. Astrophys., 9 (1970) 15-23
20. Galatolo S., Orbit complexity by computable structures, Nonlinearity, 13 (2000), no. 5, 1531-1546
21. Galatolo S., Orbit complexity and data compression, Disc. Cont. Dyn. Syst., 7 (2001), no. 3, 477-486
22. Galatolo S., Global and local Complexity in weakly chaotic dynamical systems, Disc. Cont. Dyn. Syst., 9 (2003), no. 6, 1607-1624
23. Galatolo S., Complexity, initial condition sensitivity, dimension and weak chaos in dynamical systems, Nonlinearity 16 (2003), 1219-1238
24. Gaspard P., Wang X.J., "Sporadicity: between periodic and chaotic dynamical behavior", Proc. Natl. Acad. Sci. USA, 85 (1988), 4591-4595
25. Grassberger P., Data compression and entropy estimates by non-sequential recursive pair substitution, http://arXiv.org/abs/physics/0207023
26. Katok A., Hasselblatt B., "Introduction to the modern theory of dynamical systems", Cambridge University Press, 1997
27. Khinchin A.I., "Mathematical foundations of information theory", Dover Publications, New York, 1957
28. Kolmogorov, A.N., Three Approaches to the Quantitative Definition of Information, Problems of Information Transmission, 1 (1965), no.1, 1-7
29. Kosaraju S.R., Manzini G., Compression of low entropy strings with Lempel-Ziv algorithms, SIAM J. Comput., 29 (2000), 893-911
30. Li M., Vitanyi P., "An introduction to Kolmogorov complexity and its applications", Springer-Verlag, 1993
31. Manneville P., Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems, J. Physique, 41 (1980), 1235-1243
32. Tirnakli U., Tsallis C., Lyra M.L., Circular like maps:sensitivity to initial conditions, European Phisical Journal B, 11 (1999), 309-316
33. Tsallis C., Plastino A.R., Zheng W.M., Power-law sensitivity to initial conditions - new entropic representation, Chaos Solitons Fractals, 8 (1997), no. 6, 885-891
34. Ziv J., Lempel A., A Universal Algorithm for Sequential Data Compression, IEEE Transactions on Information Theory, 23 (1977) 337-342
35. Ziv J., Lempel A., Compression of Individual Sequences Via Variable-Rate Coding, IEEE Transactions on Information Theory, 24 (1978) 530-536