Fixed point index of iterations of local homeomorphisms of the plane: a Conley index approach

Let U be an open subset of R-2 and let f : U --> R-2 be a local homeomorphism. Let p E U be a non-repeller fixed point of f such that {p} is an isolated invariant set. We introduce a particular class of index pairs for f p} that we call generalized filtration pairs. The computation of the fixed point index of any iteration of fat p is quite easy once one knows a generalized filtration pair. The existence of generalized filtration pairs provides a short and elementary proof of a theorem of P. Le Calvez and J.C. Yoccoz (Ann. of Meth. 146 (1997) 241-293), and it also allows to compute the fixed point index of any iteration of arbitrary local homeomorphisms. (C) 2002 Elsevier Science Ltd. All rights reserved.