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In a previous work, we proved an index theorem for families of asymptoticallyhyperbolic discrete dynamical systems and obtained applications to bifurcationtheory. A weaker and far more common assumption than asymptotic hyperbolicityis the existence of an exponential dichotomy. In this paper we generalize allour previous results to the latter setting, which requires substantialmodifications of our arguments. In addition, we generalize previous results oncontinuity and differentiability of Nemitski operators for discrete dynamicalsystems to obtain even better bifurcation results.

Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory