Global and local complexity in weakly chaotic dynamical systems

Discrete and Continuous Dynamical Systems

Volumn 9, Issue 6, 2003, Pages 1607-1624

  Galatolo, Stefano ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Computable analisys; Generalized orbit complexity; Generalized topological entropy; Weak chaos

Indexed keywords

EID: 0346913337     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2003.9.1607     Document Type: Article

References (27)

1. 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 Volume 13, Issue 3, March 2002
2. Benci V, Bonanno C, Galatolo S, Menconi G, Virgilio M Dynamical systems and computable information to appear on Discrete Contin. Dyn. Syst. Ser. B
3. Bonanno C., Menconi G., "Computational information for the logistic map at the chaos threshold", Discrete Contin. Dyn. Syst. Ser. B 2 (2002), no. 3, 415-431.
4. Bonanno C. Applications of information measures to chaotic dynamical systems Phd. Thesis, Dipartimento di Matematica, università di Pisa.
5. Blanchard, F.; Host, B.; Maass, A. Topological complexity. Ergodic Theory Dynam. Systems 20 (2000), no. 3, 641-662.
6. Blume, Frank. Possible rates of entropy convergence. Ergodic Theory Dynam. Systems 17 (1997), no. 1, 45-70.
7. Computability and complexity in analysis (Swansea, 2000),Edited by Jens Blanck, Vasco Brattka and Peter Hertling, Lecture Notes in Comput. Sci., 2064, Springer, Berlin, 2001.
8. Brudno A.A. Entropy and the complexity of the trajectories of a dynamical system Trans. Moscow Math. Soc. 2 127-151 (1983)
9. Chaitin G.J. Information, randomness and incompleteness. Papers on algorithmic information theory. World Scientific, Singapore 1987.
10. Collet, Pierre; Eckmann, Jean-Pierre.Iterated maps on the interval a s dynamical systems. Progress in Physics, 1. Birkhauser, Boston, Mass., 1980. vii+248 pp.
11. Fedorenko, V. V.; Sarkovskii, A. N.; Smital, J. Characterizations of weakly chaotic maps of the interval. Proc. Amer. Math. Soc. 110 (1990), no. 1, 141-148.
12. Ferenczi, S. Measure-theoretic complexity of ergodic systems. Israel J. Math. 100 (1997), 189-207.
13. Galatolo, S. Pointwise information entropy for metric spaces. Nonlinearity 12 (1999), no. 5, 1289-1298.
14. Galatolo, S. Orbit complexity by computable structures. Nonlinearity 13 (2000), no. 5, 15311546.
15. Galatolo, S. Orbit complexity and data compression Discrete and Continuous Dynamical Systems 7 (2001), no. 3, 477-486.
16. Galatolo, S. Complexity, initial condition sensitivity, dimension and weak Chaos in Dynamical Systems Nonlinearity 16 (2003), 1219-1238
17. Gaspard P., Wang X.-J., Sporadicity: between periodic and chaotic dynamical behaviors, Proc. Natl. Acad. Sci. USA 85, 4591-4595 (1988).
18. Katok, Anatole; Hasselblatt, Boris. Introduction to the modern theory of dynamical systems. With a supplementary chapter by Katok and Leonardo Mendoza. Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995.
19. Manneville P., Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems, J. Physique 41, 1235-1243 (1980).
20. Misiurewicz, Michał. Invariant measures for continuous transformations of [0,1] with zero topological entropy. Ergodic theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1978), pp. 144-152, Lecture Notes in Math., 729, Springer, Berlin, 1979.
21. Petersen K. Ergodic Theory Cambrigdge University Press, Cambridge (1983)
22. Eckmann, J.-P.; Ruelle, D. Addendum: Ergodic theory of chaos and strange attractors. Rev. Modern Phys. 57 (1985), no. 4, 1115.
23. Smital, J. Chaotic functions with zero topological entropy. Trans. Amer. Math. Soc. 297 (1986), no. 1, 269-282.
24. Takens, Floris; Verbitski, Evgeny. Generalized entropies: Renyi and correlation integral approach. Nonlinearity 11 (1998), no. 4, 771-782.
25. 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.
26. White H. Algorithmic complexity of points in dynamical systems Ergodic Theory Dynam. Syst. 13 807-830 (1993)
27. Zvorkin A.K., Levin L.A. The complexity of finite objects and the algorithmic-theoretic foundations of the notion of information and randomness Russ. Math. Surv. 25 (1970)