Computer assisted proof of chaos in the Rössler equations and in the Hénon map

Nonlinearity

Volumn 10, Issue 1, 1997, Pages 243-252

  Zgliczyński, Piotr ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041540896     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/1/016     Document Type: Article

References (13)

1. Benedicks M and Carleson L 1991 The dynamics of the Hènon map Ann. Math. 133 73-169
2. Carleson L 1990 The dynamics of non-uniformly hyperbolic systems in two variables Proc. Int. Cong. Math. (Kyoto) pp 1241-7
3. Dold A 1972 Lectures on Algebraic Topology (Berlin: Springer)
4. Hènon M 1976 A two-dimensional mapping with a strange attractor Commun. Math. Phyn. 50 69-77
5. Mischaikow K and Mrozek M 1995 Chaos in the Lorenz equations: a computer assisted proof Bull. AMS 32 66 72
6. Mischaikow K and Mrozek M 1995 Isolating neighbourhoods and chaos Japan. J. Indust. Appl. Math. 12 205 36
7. Mrozek M 1990 Leray functor and cohomological Conley for discrete dynamical systems Trans. Am. Math. Soc. 318 149-78
8. Mora L and Viana M 1993 Abundance of strange attractors Acta Math. 171 1-71
9. Rössler O E 1976 An equation for continuous chaos Phys. Lett. 57A 397-8
10. Smale S Differentiable dynamical systems Bull. Am. Math. Soc. 73 747-817
11. Zgliczyński P Fixed point index for iterations of maps, topological horseshoe and chaos Topological Meth. Nonlinear Anal. to appear
12. Zgliczyński P A computer assited proof of the horseshoe dynamics in the Hénon map Random Comput. Dynam. Sys. to appear
13. Zgliczyński P Chaos in the Rössler equations computer assisted proof, in preparation