Prevalent Dynamics at the First Bifurcation of Hénon-like Families

研究成果: Article査読

7 被引用数 (Scopus)

抄録

We study the dynamics of strongly dissipative Hénon-like maps, around the first bifurcation parameter a* at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We prove that a* is a full Lebesgue density point of the set of parameters for which Lebesgue almost every initial point diverges to infinity under positive iteration. A key ingredient is that a* corresponds to the "non-recurrence of every critical point", reminiscent of Misiurewicz parameters in one-dimensional dynamics. Adapting on the one hand Benedicks & Carleson's parameter exclusion argument, we construct a set of "good parameters" having a* as a full density point. Adapting Benedicks & Viana's volume control argument on the other, we analyze Lebesgue typical dynamics corresponding to these good parameters.

本文言語English
ページ(範囲)37-85
ページ数49
ジャーナルCommunications in Mathematical Physics
312
1
DOI
出版ステータスPublished - 2012 5月
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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