Open AccessMultiplicity of symmetric brake orbits of asymptotically linear symmetric reversible Hamiltonian systems
Author(s) -
Jiachen Mu,
Duanzhi Zhang
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022123
Subject(s) - mathematics , brake , multiplicity (mathematics) , hamiltonian system , hamiltonian (control theory) , morse code , pure mathematics , mathematical analysis , computer science , mathematical optimization , telecommunications , materials science , metallurgy
In this paper, we give the relation between a relative Morse index for two continuous symmetric matrices paths in $ {{\bf R}}^{2n} $ satisfying condition (BS1) and the Maslov-type indices under symmetric brake orbit boundary value of these two symmetric matrices paths. As application, we obtain a multiple existence of symmetric brake orbit solutions of asymptotically linear symmetric reversible Hamiltonian systems.