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

Chang Gao

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arXiv · 2206.02974

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

Chang Gao

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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.

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Chang Gao. 2022-06-07. A proof of the $C^r$ closing lemma and stability conjecture. https://arxiv.org/abs/2206.02974

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