A Comparison Principle for Bifurcation of Periodic Solutions of Hamiltonian Systems
Helene Cyris, Joanna Janczewska, Nils Waterstraat
TL;DR
This paper introduces a new comparison principle based on spectral flow to identify local bifurcations of periodic solutions in Hamiltonian systems, simplifying the detection process through coefficient inspection.
Contribution
It presents a novel comparison principle for spectral flow that facilitates the detection of bifurcations in Hamiltonian systems' periodic solutions.
Findings
New criteria for local bifurcation detection
Spectral flow comparison principle established
Simplified method for identifying solution emergence
Abstract
We obtain novel criteria for the existence of local bifurcation for periodic solutions of Hamiltonian systems by a comparison principle of the spectral flow. Our method allows to find the appearance of new solutions by a simple inspection of the coefficients of the system.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Differential Equations Analysis · Advanced Differential Equations and Dynamical Systems