The Index Bundle and Multiparameter Bifurcation for Discrete Dynamical   Systems
  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. 
Robert Skiba and Nils Waterstraat
math.FA math.DS math.KT