%0 Journal Article
%A Romero Ruiz del Portal, Francisco
%A Graff,  Grzegorz
%A Nowak-Przygodzki, Piotr
%T Local fixed point indices of iterations of planar maps
%D 2011
%@ 1040-7294
%U https://hdl.handle.net/20.500.14352/42017
%X Let f : U →R2 be a continuous map, where U is an opensubset of R2. We consider a  fixed point p of  f  which is neither a sink nora source and such that p is an isolated invariant set. Under these assumptionwe prove, using Conley index methods and Nielsen theory, that the sequence of fixed point indices of iterations ind(fn, p) n=1 is periodic,bounded by 1, and has infinitely many non-positive terms, which is a generalization of Le Calvez and Yoccoz theorem [Annals of Math., 146 (1997), 241-293] onto the class of non-injective maps. We apply our result to study the dynamics of continuous maps on 2-dimensionalsphere.
%~