Topologically Stable Chain Recurrence Classes for Diffeomorphisms

Let <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></mrow></semantics></math></inline-formula> be a diffeomorphism of a fin...

Full description

Bibliographic Details
Main Author:	Manseob Lee
Format:	Article
Language:	English
Published:	MDPI AG 2020-11-01
Series:	Mathematics
Subjects:	topologically stable chain recurrence class generic hyperbolic
Online Access:	https://www.mdpi.com/2227-7390/8/11/1912

id	doaj-48211e8164bf4676adf1d615ff2c73d7
record_format	Article
spelling	doaj-48211e8164bf4676adf1d615ff2c73d72020-11-25T03:56:17ZengMDPI AGMathematics2227-73902020-11-0181912191210.3390/math8111912Topologically Stable Chain Recurrence Classes for DiffeomorphismsManseob Lee0Department of Mathematics, Mokwon University, Daejeon 302-729, KoreaLet <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></mrow></semantics></math></inline-formula> be a diffeomorphism of a finite dimension, smooth compact Riemannian manifold <i>M</i>. In this paper, we demonstrate that if a diffeomorphism <i>f</i> lies within the <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>1</mn></msup></semantics></math></inline-formula> interior of the set of all chain recurrence class-topologically stable diffeomorphisms, then the chain recurrence class is hyperbolic.https://www.mdpi.com/2227-7390/8/11/1912topologically stablechain recurrence classgenerichyperbolic
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Manseob Lee
spellingShingle	Manseob Lee Topologically Stable Chain Recurrence Classes for Diffeomorphisms Mathematics topologically stable chain recurrence class generic hyperbolic
author_facet	Manseob Lee
author_sort	Manseob Lee
title	Topologically Stable Chain Recurrence Classes for Diffeomorphisms
title_short	Topologically Stable Chain Recurrence Classes for Diffeomorphisms
title_full	Topologically Stable Chain Recurrence Classes for Diffeomorphisms
title_fullStr	Topologically Stable Chain Recurrence Classes for Diffeomorphisms
title_full_unstemmed	Topologically Stable Chain Recurrence Classes for Diffeomorphisms
title_sort	topologically stable chain recurrence classes for diffeomorphisms
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-11-01
description	Let <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></mrow></semantics></math></inline-formula> be a diffeomorphism of a finite dimension, smooth compact Riemannian manifold <i>M</i>. In this paper, we demonstrate that if a diffeomorphism <i>f</i> lies within the <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>1</mn></msup></semantics></math></inline-formula> interior of the set of all chain recurrence class-topologically stable diffeomorphisms, then the chain recurrence class is hyperbolic.
topic	topologically stable chain recurrence class generic hyperbolic
url	https://www.mdpi.com/2227-7390/8/11/1912
work_keys_str_mv	AT manseoblee topologicallystablechainrecurrenceclassesfordiffeomorphisms
_version_	1724465879769415680

Topologically Stable Chain Recurrence Classes for Diffeomorphisms

Similar Items