Romero Ruiz del Portal, FranciscoSalazar, J. M.2023-06-202023-06-2020040166-864110.1016/j.topol.2003.12.013https://hdl.handle.net/20.500.14352/50345Let 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.engjournal articlehttp://www.sciencedirect.com/science/journal/01668641http://www.sciencedirect.comrestricted access515.1Fixed point indexConley indexFiltration pairsTopología1210 Topología