Generalization of Lyapunov Center Theorem for Hamiltonian systems via normal forms theory

2024/06/20 by Anna Gołȩbiewska, Gołębiewska, A., Sławomir Rybicki +1
Engineering · Mathematics · Physics and Astronomy · #37J20 #37J46 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Control and Stability of Dynamical Systems #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2406.14053

openalex publication_date 2024/06/20 · openalex created_date 2024/06/22 · openalex updated_date 2026/07/28

Abstract

In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions of some well-known theorems imply that of our main results. We obtain our results with the use of the theory of normal forms for Hamiltonian matrices and global bifurcation theory for autonomous Hamiltonian systems.

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