Abstract

Let $U$ be an open subset of $R2$ and $f:\; U\; \to \; f(U)\; \subset \; R2$ be a homeomorphism such that $Per(f)=p\; \subset \; U$. We give a Poincaré formula relating the fixed point indices of the iterations of $f$ at $p$ and the local dynamical behavior of $f$ in terms of the stable/unstable "manifolds" and the Leau-Fatou attracting/repelling petals of $f$ around $p$. We shall provide some applications to the study of fixed and periodic points of homeomorphisms of surfaces.