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arXiv · 2104.01586

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

Marek Izydorek·Joanna Janczewska·Nils Waterstraat
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Abstract

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.

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Marek Izydorek, Joanna Janczewska, Nils Waterstraat. 2021-04-04. The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems. https://arxiv.org/abs/2104.01586

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