A proof of the $C^r$ closing lemma and stability conjecture
C. Gao. (2022)cite arxiv:2206.02974Comment: 11 pages.
Abstract
This paper presents a proof of the $C^r$ closing lemma and stability
conjecture for flows and diffeomorphisms on locally compact Riemannian
manifolds. The dimension of the perturbation is reduced by extending the flow
box of the periodic orbit so as to control the $C^r$ size of Lie derivatives.
Density of the periodic points are hence preserved by homeomorphisms, due to
the topological invariance of structurally stable differential systems under
perturbations. Necessity of hyperbolicity of nonwandering set is proved by
contradicting the nonhyperbolic tendency of periodic points.
Description
A proof of the $C^r$ closing lemma and stability conjecture
%0 Generic
%1 gao2022proof
%A Gao, Chang
%D 2022
%K article
%T A proof of the $C^r$ closing lemma and stability conjecture
%U http://arxiv.org/abs/2206.02974
%X This paper presents a proof of the $C^r$ closing lemma and stability
conjecture for flows and diffeomorphisms on locally compact Riemannian
manifolds. The dimension of the perturbation is reduced by extending the flow
box of the periodic orbit so as to control the $C^r$ size of Lie derivatives.
Density of the periodic points are hence preserved by homeomorphisms, due to
the topological invariance of structurally stable differential systems under
perturbations. Necessity of hyperbolicity of nonwandering set is proved by
contradicting the nonhyperbolic tendency of periodic points.
@misc{gao2022proof,
abstract = {This paper presents a proof of the $C^r$ closing lemma and stability
conjecture for flows and diffeomorphisms on locally compact Riemannian
manifolds. The dimension of the perturbation is reduced by extending the flow
box of the periodic orbit so as to control the $C^r$ size of Lie derivatives.
Density of the periodic points are hence preserved by homeomorphisms, due to
the topological invariance of structurally stable differential systems under
perturbations. Necessity of hyperbolicity of nonwandering set is proved by
contradicting the nonhyperbolic tendency of periodic points.},
added-at = {2022-06-08T15:39:38.000+0200},
author = {Gao, Chang},
biburl = {https://www.bibsonomy.org/bibtex/29c0a86ed27d82988b0f02a4f7be629c0/lacerdagabo},
description = {A proof of the $C^r$ closing lemma and stability conjecture},
interhash = {5eed28be880debf2d5ece387e9a5c44a},
intrahash = {9c0a86ed27d82988b0f02a4f7be629c0},
keywords = {article},
note = {cite arxiv:2206.02974Comment: 11 pages},
timestamp = {2022-06-08T15:39:38.000+0200},
title = {A proof of the $C^r$ closing lemma and stability conjecture},
url = {http://arxiv.org/abs/2206.02974},
year = 2022
}