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A family index theorem for periodic Hamiltonian systems and bifurcation

Waterstraat, Nils (2015) A family index theorem for periodic Hamiltonian systems and bifurcation. Calculus of Variations and Partial Differential Equations, 52 . pp. 727-753. ISSN 0944-2669. (doi:10.1007/s00526-014-0731-z)

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http://www.dx.doi.org/10.1007/s00526-014-0731-z

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.

Item Type: Article
DOI/Identification number: 10.1007/s00526-014-0731-z
Additional information: Imported from arXiv
Subjects: Q Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Nils Waterstraat
Date Deposited: 03 Nov 2015 12:18 UTC
Last Modified: 29 May 2019 16:15 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51391 (The current URI for this page, for reference purposes)
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