The Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems

Skiba, Robert and Waterstraat, Nils (2017) The Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems. Discrete and Continuous Dynamical Systems. Series A, 37 (11). pp. 5603-5629. ISSN 1078-0947. E-ISSN 1553-5231. (doi:https://doi.org/10.3934/dcds.2017243) (Full text available)

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Official URL
http://dx.doi.org/10.3934/dcds.2017243

Abstract

We develop a K-theoretic approach to multiparameter bifurcation theory of homoclinic solutions of discrete non-autonomous dynamical systems from a branch of stationary solutions. As a byproduct we obtain a family index theorem for asymptotically hyperbolic linear dynamical systems which is of independent interest. In the special case of a single parameter, our bifurcation theorem weakens the assumptions in previous work by Pejsachowicz and the first author.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology > QA612 Algebraic topology
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Nils Waterstraat
Date Deposited: 17 Jan 2017 11:23 UTC
Last Modified: 04 Sep 2017 08:33 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/59892 (The current URI for this page, for reference purposes)
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