%0 Journal Article
%A Romero Ruiz del Portal, Francisco
%A Salazar, J. M.
%T Fixed point index and decompositions of planar invariant compacta
%D 2004
%@ 0166-8641
%U https://hdl.handle.net/20.500.14352/50345
%X Let U c R2 be an open subset and let f :U → f (U) c R2 be a homeomorphism. Let M = M1 U· · ·U Mr C U be a disjoint union of discs that isolates the invariant compactum K. The aimof this paper is to study the dynamics of f in K and to use the fixed point index to detect, in a simple and geometric way, the existence of periodic orbits on which f follows a determined pattern. Our method allows us to compute the fixed point index of every iteration of f in a neighborhood of the periodic orbits following a given itinerary in classical and important semidynamical systems with chaotic dynamics.
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