Rigorous numerical studies of the existence of periodic orbits for the Hénon map

Journal of Universal Computer Science

Volumn 4, Issue 2, 1998, Pages 114-124

  Galias, Zbigniew ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

Chaos; Computer assisted proof; Interval arithmetic

Indexed keywords

EID: 0007431667     PISSN: 0958695X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

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2. [Götz 94] Götz, A.; "Inclusion Methods for Systems of Nonlinear - The Interval Newton Method and Modifications"; in Topics in Validated Computations, ed. J. Herzberger, 1994, Elsevier Science B.V., 7-26.
3. [Galias 97] Galias, Z.; "Positive topological entropy of Chua's circuit: a computer assisted proof"; Int. J. Bifurcation and Chaos, 7, 2 (1997), 331-349.
4. [Galias, Zgliczyński 96] Galias, Z., Zgliczyński, P.; "Computer assisted proof of chaos in the Lorenz system", IMUJ preprint 1996/23, accepted for publication in Physica D.
5. [Guckenheimer, Holmes 83] Guckenheimer, J., Holmes, P.; "Nonlinear Oscillations,Dynamical Systems, and Bifurcations of Vector Fields"; Springer-Verlag, 1983.
6. [Hénon 76] M. Hénon; "A two dimensional map with a strange attractor"; Commun. Math. Phys., 50, 1976, 463.
7. [Robinson 95] Robinson, C.; "Dynamical Systems: Stability, Symbolic Dynamics, and Chaos"; CRC Press, Boca Raton, 1995.
8. [Knüppel 93] Knüppel, O.: "PROFIL - programmer's runtime optimized fast interval library"; Technical University Hamburg-Harburg, July 1993, Bericht 93.4.
9. [Zgliczyński 97a] P. Zgliczyński; "Computer assisted proof of the horseshoe dynamics in the Hénon map"; Random & Computational Dynamics, 5, 1 (1997), 1-19.
10. [Zgliczyński 97b] Zgliczyński, P.: "Computer assisted proof of chaos in the Rössler equations and in the Hénon map"; Nonlinearity, 10, 1 (1997), 243-252.