A proof of the $C^r$ closing lemma and stability conjecture

Chang Gao

A proof of the $C^r$ closing lemma and stability conjecture

Dynamical Systems 2023-09-15 v3 Classical Analysis and ODEs Differential Geometry

Authors: Chang Gao

Abstract

It has long been conjectured that generic dynamical systems has finite periodic orbits, ever since the time of Poincar\'e. In this article, a perturbation method is proposed for the $C^r$ closing of periodic orbits. This method is applicable to both time-varying and time-invariant vector fields.

Keywords

dynamical systems closing lemma stability conjecture periodic orbits perturbation method vector fields

Cite

@article{arxiv.2206.02974,
  title  = {A proof of the $C^r$ closing lemma and stability conjecture},
  author = {Chang Gao},
  journal= {arXiv preprint arXiv:2206.02974},
  year   = {2023}
}

Comments

A formal proof may appear for this article

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