A family index theorem for periodic Hamiltonian systems and bifurcation
Differential Geometry
2015-11-03 v2 Dynamical Systems
Functional Analysis
Symplectic Geometry
Abstract
We prove an index theorem for families of linear periodic Hamiltonian systems, which is reminiscent of the Atiyah-Singer index theorem for selfadjoint elliptic operators. For the special case of one-parameter families, we compare our theorem with a classical result of Salamon and Zehnder. Finally, we use the index theorem to study bifurcation of branches of periodic solutions for families of nonlinear Hamiltonian systems.
Keywords
Cite
@article{arxiv.1305.5679,
title = {A family index theorem for periodic Hamiltonian systems and bifurcation},
author = {Nils Waterstraat},
journal= {arXiv preprint arXiv:1305.5679},
year = {2015}
}
Comments
29 pages; v2: final version, minor changes