Spectral flow, crossing forms and homoclinics of Hamiltonian systems
Dynamical Systems
2017-05-17 v2 Differential Geometry
Functional Analysis
Symplectic Geometry
Abstract
We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of nonautonomous Hamiltonian vector fields.
Keywords
Cite
@article{arxiv.1406.3760,
title = {Spectral flow, crossing forms and homoclinics of Hamiltonian systems},
author = {Nils Waterstraat},
journal= {arXiv preprint arXiv:1406.3760},
year = {2017}
}
Comments
35 pages; v2: final version, Theorem 2.7 improved according to referee's suggestions, additional minor changes