On the bifurcation of periodic orbits

2001/10/11 by Jean-Pierre Francoise, Jean–Pierre Françoise, Francoise, Jean-Pierre
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.AG #math.DS

paper · pdf · doi:10.48550/arxiv.math/0110121

arxiv created 2001/10/11 · openalex publication_date 2001/10/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping. Explicit estimates of the size of the domain on which the number of limit cycles is controlled are important in many applications of bifurcation theory (for instance in Biology and Physiology).

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