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

Autor:	Skiba, Robert, Waterstraat, Nils
Rok vydání:	2020
Předmět:	Mathematics - Functional Analysis Mathematics - Dynamical Systems Mathematics - K-Theory and Homology
Druh dokumentu:	Working Paper
Popis:	In a previous work, we proved an index theorem for families of asymptotically hyperbolic discrete dynamical systems and obtained applications to bifurcation theory. A weaker and far more common assumption than asymptotic hyperbolicity is the existence of an exponential dichotomy. In this paper we generalize all our previous results to the latter setting, which requires substantial modifications of our arguments. In addition, we generalize previous results on continuity and differentiability of Nemitski operators for discrete dynamical systems to obtain even better bifurcation results. Comment: 34 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.12433 Zobrazit plný text záznamu View this record from Arxiv