A C2 generic trichotomy for diffeomorphisms: hyperbolicity or zero Lyapunov exponents or the C1 creation of homoclinic bifurcations
A C2 generic trichotomy for diffeomorphisms: hyperbolicity or zero Lyapunov exponents or the C1 creation of homoclinic bifurcations
复制标题
微分同胚的 C2 通用三分法：双曲性或零 Lyapunov 指数或同宿分岔的 C1 创建
DOI：
10.1090/s0002-9947-2014-06425-8
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发表时间：
2014
影响因子：
1.3
通讯作者：
Shuhei HAYASHI
中科院分区：
文献类型：
--
作者：
伊藤 隆;渚 勝;剱持勝衛;Shuhei HAYASHI
Palis推测密集的差同形要么是双曲的，要么表现出同斜分叉。我们证明了微分同态的一般三分法：一个无环或库普卡-小环的微分同态的公理a，允许零Lyapunov指数，或产生同斜分岔（即，由一些小扰动产生同斜切线或异维环）。参考文献
Palis conjectured that densely in,, diffeomorphisms are either hyperbolic or exhibit homoclinic bifurcations. We prove a generic trichotomy fordiffeomorphisms: an Axiom A diffeomorphism with no cycles or Kupka-Smale ones admitting zero Lyapunov exponents or thecreation of homoclinic bifurcations (ie, the creation of homoclinic tangencies or heterodimensional cycles by somesmall perturbations). References