Publication: A Poincare Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms
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2010
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Hindawi Publishing Coporation
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Abstract
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.
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Dedicated to professor José M. Montesinos in the occasion of his 65th birthday and to the memory of professor Julián Martínez.
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