A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms
© F. R. Ruiz del Portal and J. M. Salazar. 2010
Received: 11 November 2009
Accepted: 1 March 2010
Published: 18 May 2010
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.
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