Shadowing properties of L-hyperbolic homeomorphisms

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• 作者：Sakai ; Kazuhiro
• 关键词：L-hyperbolic homeomorphism ; Pseudo-orbit ; Shadowing property ; Lipschitz shadowing property ; Average shadowing property ; Compact metric space ; Axiom A diffeomorphism ; 37B99 ; 37C15 ; 37C50 ; 37D20 ; 54H20 ; 37H99
• 刊名：Topology and its Applications
• 出版年：2001
• 出版时间：June 15, 2001
• 年：2001
• 卷：112
• 期：3
• 页码：229-243
• 全文大小：145 K

文摘

We introduce the notion of L-hyperbolic homeomorphisms on compact metric spaces as a strict generalization of Axiom A diffeomorphisms and prove that the notion is equivalent to expansive homeomorphisms having the shadowing property and to Ruelle's Smale spaces. Furthermore, for L-hyperbolic homeomorphisms, both the Lipschitz shadowing property and the average shadowing property are shown.