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The index bundle and multiparameter bifurcation for discrete dynamical systems

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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.

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

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