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Autor Romero Ruiz del Portal, Francisco |
Documentos disponibles escritos por este autor (48)
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Hernández Corbato, Luis ; Le Calvez , Patrice ; Romero Ruiz del Portal, Francisco | Geometry & Topology Publications, Univ Warwick, Mathematics Inst | 2013This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism f in R-d and an acyclic continuum X, such as a cellular set or a fixed point, invariant under f [...]![]()
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Cuchillo Ibáñez, Eduardo ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco | Editorial Complutense | 1994This interesting and well-written survey article is devoted to the class P of topological spaces in which components and quasi-components coincide. This class includes the compact Hausdorff spaces and the locally connected spaces. It also inclu[...]![]()
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Carabantes Alarcón, David ; Ancochea Soto, Eumenio ; Arias Astray, Andrés ; Dupont Sfez, Samuelle ; Iglesias Recuero, Silvia ; Manjón-Cabeza Olmeda, Araceli ; Martín Martín, José Oliver ; Montero de Juan, Francisco Javier ; Romero Ruiz del Portal, Francisco ; San Andrés Moya, Margarita ; Sastre Castillo, Miguel Ángel ; Tirado Fernández, Francisco | 2018-06-30El Aprendizaje Servicio es una estrategia docente necesaria para el desarrollo de iniciativas de emprendimiento e innovación social, que partan desde la Universidad, y que se puedan incorporar en las diferentes áreas de conocimiento de la UCM![]()
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Hernández Corbato, Luis ; Ortega, Rafael ; Romero Ruiz del Portal, Francisco | Cambridge Univ Press | 2012Let h : R-2 -> R-2 be a dissipative and orientation preserving homeomorphism having an asymptotically stable fixed point. Let U be the region of attraction and assume that it is proper and unbounded. Using Caratheodory's prime ends theory one c[...]![]()
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Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a[...]![]()
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A bimorphism is both an epimorphism and a monomorphism. If every bimorphism is an iso then the given category is said to be balanced. Such notions are studied in several contexts (pro-categories, pro-homotopy, shape, proper homotopy). The refere[...]![]()
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The authors deal with the question of whether the sets of shape and homotopy types of FANRs are countable. FANRs can be considered as a natural generalization of ANRs; thus the authors' starting point consists of results on the countability of t[...]![]()
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Giraldo, A. ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science B.V. (North-Holland) | 2001-09-07We show in this paper how to represent intrinsically Cech homology of compacta, in terms of inverse limits of discrete approximations. We establish some relations between inverse limits and non-continuous homotopies and, as a consequence, we get[...]![]()
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The author proves that if f is an orientation reversing homeomorphism of the plane and p is an isolated and stable fixed point of f then the fixed point index of f at p is equal to 1 . In the orientation preserving case this result was obta[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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Hernández Corbato, Luis ; Romero Ruiz del Portal, Francisco | American Institute of Mathematical Sciences | 2015-07We characterize the sequences of fixed point indices {i(f(n) ,p)} n > = 1 of fixed points that are isolated as an invariant set for a continuous map f in the plane. In particular, we prove that the sequence is periodic and i(f(n) ,p) = 0. This[...]![]()
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In this paper we apply the generalized degree introduced by Geba, Massabo and Vignoli, in [3], to extend the notion of complementing maps defined by Fitzpatrick, Massabo and Pejsachowicz, in [1] and [2]. On the other hand, we obtain, in low dime[...]![]()
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We present a generalized degree theory for continuous maps f (D, 9D) - (E, E\{0}), where E is a normed vectorial space, Dis an open subset of Rk xEsuch that p, (D) is bounded in Rk and f is a compact perturbation of the second projection p2 : Rk[...]![]()
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The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. In (Dydak and Ruiz del Portal (Monomorphisms and epimorphisms in pro-categories, preprint)) we gave characterizations of monomorphisms (re[...]![]()
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Let f : U ?R2 be a continuous map, where U is an open subset of R2. We consider a fixed point p of f which is neither a sink nor a source and such that ?p? is an isolated invariant set. Under these assumption we prove, using Conley index meth[...]![]()
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Cuchillo Ibáñez, Eduardo ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco | Auburn University | 1992In this paper we use the lower semifinite topology in hyperspaces to obtain examples in topology such as pseudocompact spaces not countably compact, separable spaces not Lindelöf and in a natural way many spaces appear which are T0 but not T1. W[...]![]()
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A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. We give haracterizations of monomorphisms (respectively, epimorphisms) in pro-category pro-C, provided C has direct sums (respectively,pus[...]![]()
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Morón, Manuel A. ; Romero Ruiz del Portal, Francisco | Japanese Association of mathematical Sciences | 1994We give a new description of the shape category of paracompact spaces in terms of multivalued maps that allows us to find new characterizations, in some way intrinsic, of calmness, movability and maps inducing shape equivalences, and to extend t[...]![]()
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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 [...]