σ2-chaos in iterates of the classical hénon mapping

Balázs Bánhelyi, Tibor Csendes, Barnabas M. Garay

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The k-th iterate of the classical Hénon mapping has σ2-chaos in the trapping region if and only if k = 2, k = 4, or k ≥ 6. For k ≥ 13, the result is derived from case k= 12 via reconsidering Smale's fundamental theorem on the existence of topological horseshoes in the vicinity of a transversal homoclinic saddle. For k ≤ 12, the proof is computer-assisted.

Original languageEnglish
Title of host publicationNumerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
Pages857-860
Number of pages4
DOIs
Publication statusPublished - Nov 26 2009
EventInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece
Duration: Sep 18 2009Sep 22 2009

Publication series

NameAIP Conference Proceedings
Volume1168
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
CountryGreece
CityRethymno, Crete
Period9/18/099/22/09

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Keywords

  • Computer-assisted proof
  • Global optimization
  • Homoclinic saddle
  • Hénon-mapping

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Bánhelyi, B., Csendes, T., & Garay, B. M. (2009). σ2-chaos in iterates of the classical hénon mapping. In Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 (pp. 857-860). (AIP Conference Proceedings; Vol. 1168). https://doi.org/10.1063/1.3241614