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

2022/06/07 by Gao, Chang
#37C20(Primary) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.02974

Abstract

It has long been conjectured that generic dynamical systems has finite periodic orbits, ever since the time of Poincaré. 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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