Local and Global Bifurcation for Periodic Solutions of Hamiltonian Systems via Comparison Theory for the Spectral Flow

2024/12/26 by Joanna Janczewska, Janczewska, Joanna, Maciej Starostka +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2412.19271

openalex publication_date 2024/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain local and global bifurcation for periodic solutions of Hamiltonian systems by using a new way to apply a comparison principle of the spectral flow that was originally introduced by Pejsachowicz in a joint work with the third author. A particular novelty is the study of global bifurcation, which to the best of our knowledge has not been done via the spectral flow.

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