Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Hénon map

Nonlinearity

Volumn 14, Issue 5, 2001, Pages 909-932

  Galias, Zbigniew ^a,c   Zgliczyński, Piotr ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b JAGIELLONIAN UNIVERSITY   (Poland)

^c AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035622331     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/5/301     Document Type: Article

References (21)

1. Bowen R 1971 Periodic points and measures for axiom A diffeomorphisms Trans. Am. Math. Soc. 154 377-97
2. Galias Z 1998 Rigorous numerical studies of the existence of periodic orbits for the Hénon map J. Universal Comput. Sci. 4 114-24 (http://www.iicm.edu/jucs_4_2)
3. Galias Z 1999 All periodic orbits with period n ≤ 26 for the Hénon map Proc. Eur. Conf. on Circuit Theory and Design, ECCTD 99 vol 1 (Stresa) pp 361-4
4. Galias Z 2001 Interval methods for rigorous investigations of periodic orbits 11 Int. Bifurc. J. Chaos to appear
5. Gantmacher F R 1959 Applications of the Theory of Matrices (New York: Interscience)
6. Grassberger P and Kantz H 1985 Generating partitions for the dissipative Hénon map Physica 17 D 235-8
7. Grassberger P, Kantz H and Moenig U 1989 On the symbolic dynamics of the Hénon map J. Phys. A: Math. Gen. 22 5217-30
8. Hénon M 1976 A two dimensional map with a strange attractor Commun. Math. Phys. 50 69-77
9. Knüppel O 1993 Profil - programmer's runtime optimized fast interval library Technical Report 93.4, Technical University Hamburg, Harburg
10. Misiurewicz M and Szewc B 1980 Existence of a homoclinic point for the Hénon map Commun. Math. Phys. 75 285-91
11. Neumaier A 1990 Interval Methods for Systems of Equations (Cambridge: Cambridge University Press)
12. Newhouse S 1988 Entropy and volume Ergod. Theor. Dynam. Syst. 8 283-99
13. Newhouse S and Pignataro T 1993 On the estimation to topological entropy J. Stat. Phys. 72 1331-51
14. Robinson C 1995 Dynamical Systems: Stability, Symbolic Dynamics and Chaos (Boca Raton, FL: Chemical Rubber Company)
15. Stoffer D and Palmer K 1999 Rigorous verification of chaotic behavior of maps using validated shadowing Nonlinearity 12 1683-98
16. Szymczak A 1997 A combinatorial procedure for finding isolating neighbourhoods and index pairs Proc. R. Soc. Edin. A 127 1075-88
17. Viana M 1998 Dynamics: a probabilistic and geometric perspective Proc. ICM 98 (Berlin)
18. Zgliczyński P 1997 Computer assisted proof of chaos in the Rössler equations and the Hénon map Nonlinearity 10 243-52
19. Zgliczyński P 1999 Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii ordering Int. J. Bifurc. Chaos 9 1867-76
20. Zgliczyński P 1999 Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps Ergod. Theor. Dynam. Syst. 19 1655-84
21. Zgliczyński P 2001 On periodic points for systems of weakly coupled 1-dim maps Nonlin. Anal. TMA