The index bundle and multiparameter bifurcation for discrete dynamical systems

Robert Skiba; Nils Waterstraat

doi:10.3934/dcds.2017243

Article Contents

2017, Volume 37, Issue 11: 5603-5629. Doi: 10.3934/dcds.2017243

This issue Previous Article Infinitely many positive solutions of fractional nonlinear Schrödinger equations with non-symmetric potentials Next Article The initial-boundary value problems for a class of sixth order nonlinear wave equation

The index bundle and multiparameter bifurcation for discrete dynamical systems

Robert Skiba^1, and
Nils Waterstraat^2,

1.
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Torun, Poland
2.
School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, United Kingdom

Received: February 28, 2017

Revised: April 30, 2017

Published: October 2017

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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.

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Mathematics Subject Classification: Primary: 58E07; Secondary: 37C29, 19L20, 47A53.

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