Persistent homoclinic tangencies in the Hénon family

Ittai Kan, Hüseyin Koçak, James A. Yorke

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Homoclinic tangencies in the Hénon family fθ{symbol} (x, y) = (λ - x2 + by, x) for the parameter values b = 0.3 and λ ε{lunate} [1.270, 1.420] are investigated. Our main observation is that there exist three intervals comprising 93 percent of the values of the parameter λ such that for a dense set of parameter values in these intervals the Hénon family possesses a homoclinic tangency. Therefore, one should expect long parameter intervals where the Hénon family is not structurally stable. Strong numerical support for this observation is provided.

Original languageEnglish (US)
Pages (from-to)313-325
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume83
Issue number4
DOIs
StatePublished - Jun 1 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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