A Poincare Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms

作者：Ruiz del Portal Francisco R; Salazar Jose M

来源：Fixed Point Theory and Applications, 2010, 323069.

DOI：10.1155/2010/323069

Let U subset of R(2) be an open subset and f : U -> R(2) be an arbitrary local homeomorphism with Fix(f) = {p}. We compute the fixed point indices of the iterates of f at p, i(R2)(f(k), p), and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincare 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.

• 出版日期2010