Diffeomorphisms with Shadowable Measures

Diffeomorphisms with Shadowable Measures

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 <inline-formula> <math display="inline">...

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Main Authors: Kazumine Moriyasu, Kazuhiro Sakai, Naoya Sumi
Format: Article
Language:English
Published: MDPI AG 2018-12-01
Series:Axioms
Subjects:
shadowing property
pseudo-orbit
shadowable measure
Axiom A
no-cycle condition
strong transversality condition
Online Access:https://www.mdpi.com/2075-1680/7/4/93
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spelling doaj-f2f0ccb10dfa41acb171780c609187522020-11-24T21:23:02ZengMDPI AGAxioms2075-16802018-12-01749310.3390/axioms7040093axioms7040093Diffeomorphisms with Shadowable MeasuresKazumine Moriyasu0Kazuhiro Sakai1Naoya Sumi2Department of Mathematics, Tokushima University, Tokushima 770-8502, JapanDepartment of Mathematics, Utsunomiya University, Utsunomiya 321-8505, JapanDepartment of Mathematics, Kumamoto University, Kumamoto 860-8555, JapanIn 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 <inline-formula> <math display="inline"> <semantics> <msup> <mi>C</mi> <mn>1</mn> </msup> </semantics> </math> </inline-formula>-interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity.https://www.mdpi.com/2075-1680/7/4/93shadowing propertypseudo-orbitshadowable measureAxiom Ano-cycle conditionstrong transversality condition
collection DOAJ
language English
format Article
sources DOAJ
author Kazumine Moriyasu
Kazuhiro Sakai
Naoya Sumi
spellingShingle Kazumine Moriyasu
Kazuhiro Sakai
Naoya Sumi
Diffeomorphisms with Shadowable Measures
Axioms
shadowing property
pseudo-orbit
shadowable measure
Axiom A
no-cycle condition
strong transversality condition
author_facet Kazumine Moriyasu
Kazuhiro Sakai
Naoya Sumi
author_sort Kazumine Moriyasu
title Diffeomorphisms with Shadowable Measures
title_short Diffeomorphisms with Shadowable Measures
title_full Diffeomorphisms with Shadowable Measures
title_fullStr Diffeomorphisms with Shadowable Measures
title_full_unstemmed Diffeomorphisms with Shadowable Measures
title_sort diffeomorphisms with shadowable measures
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2018-12-01
description 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 <inline-formula> <math display="inline"> <semantics> <msup> <mi>C</mi> <mn>1</mn> </msup> </semantics> </math> </inline-formula>-interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity.
topic shadowing property
pseudo-orbit
shadowable measure
Axiom A
no-cycle condition
strong transversality condition
url https://www.mdpi.com/2075-1680/7/4/93
work_keys_str_mv AT kazuminemoriyasu diffeomorphismswithshadowablemeasures
AT kazuhirosakai diffeomorphismswithshadowablemeasures
AT naoyasumi diffeomorphismswithshadowablemeasures
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