$C^1$-maps having hyperbolic periodic points

Tom 169 / 2001

N. Aoki, Kazumine Moriyasu, N. Sumi Fundamenta Mathematicae 169 (2001), 1-49 MSC: Primary 37C20, 37D20, 34D30. DOI: 10.4064/fm169-1-1

Streszczenie

We show that the $C^1$-interior of the set of maps satisfying the following conditions:

(i) periodic points are hyperbolic,

(ii) singular points belonging to the nonwandering set are sinks,

coincides with the set of Axiom A maps having the no cycle property.

Autorzy

  • N. AokiDepartment of Mathematics
    Tokyo Metropolitan University
    Minami-Ohsawa 1-1, Hachioji-Shi
    Tokyo 192-0397, Japan
    and
    Faculty of Commerce
    Chuo University
    Hachioji-shi
    Tokyo 192-0393, Japan
  • Kazumine MoriyasuDepartment of Mathematics
    Tokushima University
    Minamijosanjima 1-1
    Tokushima 770-8502, Japan
    e-mail
  • N. SumiDepartment of Mathematics
    Tokyo Metropolitan University
    Minami-Ohsawa 1-1, Hachioji-Shi
    Tokyo 192-0397, Japan
    e-mail

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