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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 fix[...]texto impreso
Let X be a locally compact metric absolute neighbourhood retract for metric spaces, U subset of X be an open subset and f:U --> X be a continuous map. The aim of the paper is to study the fixed point index of the map that f induces in the hypers[...]texto impreso
Let X be a locally compact metric absolute neighbourhood retract for metric spaces, U?X be an open subset and f :U?X be a continuous map. The aim of the paper is to study the fixed point index of the map that f induces in the y perspace of X. Fo[...]texto impreso
Let U be an open subset of R2 and let f :U ? R2 be a local homeomorphism. Let p € U be a non-repeller 4xed point of f suchth at {p} is an isolated invariant set. We introduce a particular class of index pairs for {p} that we call generalized 4lt[...]texto impreso
Let U subset of R-2 be an open subset, f : U -> f (U) subset of R-2 be an orientation reversing homeomorphism and let 0 is an element of U be an isolated, as a periodic orbit, fixed point. The main theorem of this paper says that if the fixed p[...]texto impreso
Le Calvez, Patrice ; Romero Ruiz del Portal, Francisco ; Salazar, J. M. | Oxford University Press | 2010Let U subset of R-3 be an open set and f : U -> f(U) subset of R-3 be a homeomorphism. Let p is an element of U be a fixed point. It is known that if {p} is not an isolated invariant set, then the sequence of the fixed-point indices of the iter[...]texto impreso
Le Calvez , Patrice ; Romero Ruiz del Portal, Francisco ; Salazar, J. M. | Oxford University Press | 2010Let U ? R3 be an open set and f : U ? f(U) ? R3 be a homeomorphism. Let p ? U be a fixed point. It is known that if {p} is not an isolated invariant set, then the sequence of the fixedpoint indices of the iterates of f at p, (i(fn, p))n1, is, in[...]texto impreso
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. Ther[...]texto impreso
The main goal of this paper is to prove that for each n > 2, every sequence of integers satisfying Dold’s congruences is realized as the sequence of fixed point indices of the iterates of an orientation preserving Rn-homeomorphism at an isolate[...]texto impreso
We extend the shape index, introduced by Robbin and Salamon and Mrozek, to locally defined maps in metric spaces. We show that this index is additive. Thus our construction answers in the affirmative two questions posed by Mrozek in [12]. We als[...]texto impreso
We use a notion (introduced in Topology 41 (2002), 1119–1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed.
