Copyright © 2010 Francisco R. Ruiz del Portal and José M. Salazar. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be an open subset and be an arbitrary local homeomorphism with
. We compute the fixed point indices of the
iterates of at , and we
identify these indices in dynamical terms. Therefore, we obtain a
sort of Poincaré index formula without differentiability
assumptions. Our techniques apply equally to both orientation
preserving and orientation reversing homeomorphisms. We present
some new results, especially in the orientation reversing case.