Differentiable maps having hyperbolic sets

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• 作者：Aoki ; Nobuo ; Moriyasu ; Kazumine ; Oka ; Masatoshi
• 关键词：Differentiable map ; Axiom A ; Strong transversality ; 58F15
• 刊名：Topology and its Applications
• 出版年：1998
• 出版时间：January 23, 1998
• 年：1998
• 卷：82
• 期：1-3
• 页码：15-48
• 全文大小：1.27 M

文摘

We show that the set of all C^r-differentiable maps satisfying both Axiom A and the strong transversality is open with respect to the C^r-topology (r ≥ 1). This was proved by Newhouse and Palis for the class of C^r-diffeomorphisms. However, it also is obtained from the structural stability theorem for C^r-diffeomorphisms by Robbin and Robinson.