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Autor Romero Ruiz del Portal, Francisco |
Documentos disponibles escritos por este autor (48)
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We state in a short way a result that improves one of the main theorems in a paper of M. Gobbino concerning the topological properties that the phase space induces in an attractor of a discrete dynamical system.![]()
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Cuchillo Ibáñez, Eduardo ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco | Akadémiai Kiadó | 1999Given a Tychonov space X we can construct another space Y with the same group of homeomorphisms such that X and Y are: in some sense, "almost arbitrarily different".![]()
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Romero Ruiz del Portal, Francisco | Univ. Tsukuba Institute of Mathematics Tsukuba-shi Ibaraki | 1993“We present a generalized degree for maps between manifolds via framed bordism theory.We study when the degree of a map can be considered as an element of a homotopy group of spheres. Finally, we apply this tool to prove a result concerning the [...]![]()
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The classical theory of the degree of a map f: Sn !Sn has been extended by many authors. K. G ‘ eba, I. Massab`o and A. Vignoli [in Nonlinear functional analysis and its applications (Maratea,1985), 55–73, Reidel, Dordrecht, 1986; have defined a[...]![]()
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We prove that weak shape equivalences are monomorphisms in the shape category of uniformly pointed movable continua Sh(M). We use an example of Draper and Keesling to show that weak shape equivalences need not be monomorphisms in the shape categ[...]![]()
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Let WCR2 be an open subset and f :W-f ðWÞCR2 be an orientation reversing homeomorphism. We prove that if pAW is an isolated and stable fixed point of f then the fixed point index of f at p; iR2 ð f ; pÞ; is 1. We apply our theorem to the study o[...]![]()
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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[...]![]()
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Romero Ruiz del Portal, Francisco ; Giraldo, A. ; Jimenez, R. ; Morón, Manuel A. ; Rodríguez Sanjurjo, José Manuel | Elsevier | 2011In this paper we consider two notions of attractors for semidynamical systems de ned in metric spaces. We show that Borsuk's weak and strong shape theories are a convenient framework to study the global properties which the attractor inherits fr[...]![]()
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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[...]![]()
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Let X and Y be metric compacta, Y embedded in the Hilbert cube Q. For two maps f,g:X?Q the authors define F(f,g):=inf{?> 0:f is homotopic to g in the ?-neighborhood of Y}, and a sequence of maps fk :X?Q, k?N, is said to be a Cauchy sequence prov[...]![]()
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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[...]![]()
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Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 1994-02-21We use N-compactifications of 0-dimensional spaces to obtain a new shape invariant for the class of all topological spaces. We also point out that the shape and topological classifications are not the same in the realm of Tychonov spaces having [...]![]()
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Giraldo, A. ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Pergamon-Elsevier Science | 2005-02In this paper, we apply the notion and properties of compactly generated shape to study attractors in topological spaces.![]()
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Giraldo, A. ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 2001-06-29We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting[...]![]()
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The study of the stability of a periodic solution p of a vector field using either the linear variational equations (associated to the vector field at p ), or the Poincaré map on a cross section, is known to present some difficulties. This work[...]![]()
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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.![]()
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Chocano Feito, Pedro José ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco | Springer | 2020-11-23Given a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version[...]![]()
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Cuchillo Ibáñez, Eduardo ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 1999-06-09We introduce a topology on the set of shape morphisms between arbitrary topological spaces X, Y, Sh(X, Y). These spaces allow us to extend, in a natural way, some classical concepts to the realm of topological spaces. Several applications are gi[...]![]()
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In this paper we construct many generalizad ultrametrics in the sets of shape morphisms between topological spaes. We recognize a topology in these sets which is independen on the shape representation of the spaces. We construct valuations an se[...]![]()
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We apply a Cantor completion process to construct a complete, non-Archimedean metric on the set of shape morphisms between pointed compacta. In the case of shape groups we obtain a canonical norm producing a complete, both left and right invaria[...]![]()
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Blanco Gómez, Eduardo ; Hernández Corbato, Luis ; Romero Ruiz del Portal, Francisco | BIRKHAUSER VERLAG AG | 2016A characterization of dynamically defined zeta functions is presented. It comprises a list of axioms, natural extension of the one which characterizes topological degree, and a uniqueness theorem. Lefschetz zeta function is the main (and proved [...]