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Axioms 2018, 7(4), 93; https://doi.org/10.3390/axioms7040093

Diffeomorphisms with Shadowable Measures

1
Department of Mathematics, Tokushima University, Tokushima 770-8502, Japan
2
Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505, Japan
3
Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan
*
Author to whom correspondence should be addressed.
Received: 8 November 2018 / Accepted: 5 December 2018 / Published: 7 December 2018
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
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Abstract

In this paper, the notion of shadowable measures is introduced as a generalization of the shadowing property from the measure theoretical view point, and the set of diffeomorphisms satisfying the notion is considered. The dynamics of the C 1 -interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity. View Full-Text
Keywords: shadowing property; pseudo-orbit; shadowable measure; Axiom A; no-cycle condition; strong transversality condition shadowing property; pseudo-orbit; shadowable measure; Axiom A; no-cycle condition; strong transversality condition
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Moriyasu, K.; Sakai, K.; Sumi, N. Diffeomorphisms with Shadowable Measures. Axioms 2018, 7, 93.

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