Scholarlink

<p>We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic Hénon-like map and study bifurcations of the first-return maps in generic two-parameter families.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

2-Elliptic Periodic Orbits near a Nonsimple Homoclinic Tangency in Four-Dimensional Symplectic Maps

  • 期刊论文

  • 发表日期：

    2026年5月28日

查看全文
  • Sergey Gonchenko,
  • Lev Lerman,
  • Dmitry Turaev

摘要

We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic Hénon-like map and study bifurcations of the first-return maps in generic two-parameter families.