Topological entropy and Arnold complexity for two-dimensional mappings

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 262, Issue 1, 1999, Pages 44-49

  Abarenkova, N ^a,b   Angles D'Auriac J Ch ^a   Boukraa, S ^c   Hassani, S ^d   Maillard, J M ^e  

^a Ctr Recher Ches sur les Tres B   (France)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^c UNIVERSITY OF BLIDA   (Algeria)

^d Research Centre CDTN   (Algeria)

^e LPTHE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; MAPPING; NUMERICAL METHODS; RATIONAL FUNCTIONS;

COMPLEX VARIABLE; COMPLEXITY GROWTH; GENERATING FUNCTIONS; INTEGER COEFFICIENT; RATIONAL EXPRESSIONS; TOPOLOGICAL ENTROPY; TWO DIMENSIONAL MAPPING; TWO PARAMETER;

TOPOLOGY;

EID: 0007234202     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(99)00662-3     Document Type: Article

References (23)

1. E. Ott, Chaos in dynamical systems, Cambridge University Press, 1993.
2. K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos: An introduction to dynamical systems, Springer-Verlag, New York, 1997.
3. A.N. Kolmogorov, Dokl. Acad. Nauk SSSR 119 (1958) 861.
4. Ya.G. Sinai, Dokl. Acad. Nauk SSSR 124 (1959) 768.
5. R.C. Adler, A.C. Konheim, M.H. McAndrew, Trans Am. Math. Soc. 114 (1965) 309.
6. V. Arnold, Problems on singularities and dynamical systems, in: V. Arnold, M. Monastyrsky (Eds), Developments in Mathematics: The Moscow School Chapman & Hall, Chp. 7, 1989, pp. 261-274.
7. V. Baladi, Ergod. Th. & Dyn. Sys 18 (1998) 255.
8. D. Ruelle, IHES preprint: IHES/P/91/56.
9. M. Artin, B. Mazur, Ann. of Math. 81 (1965) 82.
10. C. Smale, Bull. Amer. Math. Soc. 73 (1967) 747.
11. Chaos Classical and Quantum: a Web book to be found in Cvitanovic's web site, http://www.nbi.dk/ChaosBook.
12. V.I. Arnold, A. Avez, Problèmes ergodiques de la mécanique classique. Gauthier-Villars, Paris, 1967.
13. R. Mainieri, Phys Rev. Lett. 68 (1992) 1965.
14. M.J. Feigenbaum, J. Stat. Phys 19 (1978) 25.
15. S. Boukraa, J-M. Maillard, G. Rollet, Physica A 208 (1994) 115.
16. S. Boukraa, J-M. Maillard, Physica A 220 (1995) 403.
17. M. Bellon, C.M. Viallet chao-dyn/9805006 v2.
18. S. Boukraa, J-M. Maillard, G. Rollet, J. Stat. Phys. 78 (1995) 1195.
19. S. Boukraa, S. Hassani, J-M. Maillard, Physica. A 240 (1997) 586.
20. N. Abarenkova et al., in preparation.
21. The multi-precision library gmp is part of the GNU project.
22. N. Abarenkova, J.C. Angles d'Auriac, S. Boukraa, S. Hassani and J-M. Maillard, chao-dyn/9807014.
23. N. Abarenkova et al., in preparation.