The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems

Autor:	Izydorek, Marek, Janczewska, Joanna, Waterstraat, Nils
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Mathematics - Dynamical Systems Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This $G$-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the $G$-equivariant spectral flow to study bifurcation of periodic solutions for autonomous Hamiltonian systems with symmetries. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.01586 Zobrazit plný text záznamu View this record from Arxiv