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Autor Rodríguez Sanjurjo, José Manuel |
Documentos disponibles escritos por este autor (61)
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Some properties of movable compacta are given in aonnection with quasi-dominación and likeness. The main result is the following : Let X,Y be two comnacta. If Y is movable and X-like then Y is quasi-dominated by X.![]()
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We give in this paper a description of the shape category of compacta in terms of multivalued maps. We introduce the notion of a multi-net and prove that the shape category of compacta is isomorphic to the category HN whose objects are metric co[...]![]()
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Some extension properties of maps defined on dense subsets are studied for approximate polyhedra. The latter are characterised as approximate extensors for finite maps with small oscillation.![]()
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The aim of this paper is to present a brief survey of some aspects of the theory of approximative retracts. We put special emphasis on properties of approximative absolute neighborhood retracts (both in the sense of Noguchi and in the sense of C[...]![]()
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This paper is devoted to the study of some aspects of the stability theory of flows. In particular, we study Morse decompositions induced by non-saddle sets, including their corresponding Morse equations, attractor-repeller splittings of non-sad[...]![]()
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We show in this paper that the category of shape can be modelled in discrete terms using maps defined in dense subsets of compacta. This approach to shape provides in addition a characterization of the shape of compacta which does not require ex[...]![]()
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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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We define a semidynamical system - inspired by some classical dynamical systems studied by Bebutov in function spaces - in the space of approximative maps A(X, Y) between two metric compacta, with a suitable metric. Shape and strong shape morphi[...]![]()
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Fernández Laguna, Víctor ; Morón, Manuel A. ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 1991-07-31In this paper we study certain shape and homotopy properties of refinable and weakly refinable maps. In particular we give a sufficient condition for a weakly refinable map to be a homotopy domination when the codomain is an ANR. We also charact[...]![]()
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Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Addison-Wesley Iberoamericana España | 1998Este libro presenta, de modo directo y accesible, las nociones y los resultados básicos de la geometría proyectiva: variedades y aplicaciones proyectivas, razón doble, homografías y cuádricas. La exposición teórica se completa con notas históric[...]![]()
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We study the homotopical and homological properties of the attractors evolving from a generalized Hopf bifurcation. We consider the Lorenz equations for parameter values near the Hopf bifurcation and study a natural Morse decomposition of the gl[...]![]()
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We introduce the notion of internal fundamental sequence and prove that any shape morphism from an arbitrary compactum X to an internally movable compactum Y is induced by an internal fundamental sequence. We use this special kind of fundamental[...]![]()
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We study in this paper some properties of the Lusternik-Schnirelmann category of isolated invariant sets of continuous dynamical systems. There are several different definitions of this coefficient, although most of them agree in the important c[...]![]()
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We establish an inequality relating the Lusternik-Schnirelmann coefficient of the unstable manifold of an isolated invariant set of a flow and the coefficients of a Morse decomposition of this set. We also establish some homological relations be[...]![]()
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Castrillón López, Marco ; Martín Peinador, Elena ; Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Departamento de Geometría y Topología | 2015-09This volume contains the contributions presented by several colleagues as a tribute to the mathematical and human qualities of José María Montesinos Amilibia on the occasion of his seventieth birthday. The editors would like to express their tha[...]![]()
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We describe a new way of obtaining the Morse equations of a Morse decomposition of an isolated invariant set. This is achieved through a filtration of truncated unstable manifolds associated with the decomposition. The results in the paper make [...]![]()
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The notion of a non-saddle decomposition of a compact ANR is introduced. This notion extends that of a an attractor-repeller pair. Some cohomological properties of non-saddle decompositions are studied. In particular, some inequalities in the sp[...]![]()
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Fernández Laguna, Víctor ; Morón, Manuel A. ; Nhu, Nguyen Tho ; Rodríguez Sanjurjo, José Manuel | Polish acad sciences inst mathematics | 1993We define a metric d(S), called the shape metric, on the hyperspace 2X of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyh[...]![]()
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Giraldo, A. ; Rodríguez Sanjurjo, José Manuel | Mathematical Institute of the Academy of Sciences of the Czech Republic | 2001In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration[...]![]()
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Recently, the author has given an alternate (and intrinsic) description of the shape category of metric compacta, based on the notion of multi-nets F:X?Y. These are defined as sequences (Fk) of upper semicontinuous multivalued mappings Fk:X?Y, w[...]![]()
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Under suitable hypotheses the well known notion of first prolongational set J(+) gives rise to a multivalued map Psi : X -> 2(X) which is continuous when the upper semifinite topology is considered in the hyperspace of X. Some important dynamic[...]![]()
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Given two shape morphisms F,G:X?Y , where X and Y are compacta, one declares F to be a divisor of G provided for any compactum Z and any shape morphism U:X?Z if F factors as F=F 1 ?U , then G factors as G=G 1 ?U . On the other hand, if S[...]![]()
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The author introduces the notion of an ? -fundamental retraction which combines conditions that are used in Borsuk's shape theory, the reviewer's approximate shape theory, and Bogatyi's internal shape theory. This concept is used to define a cla[...]![]()
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In ANR theory, the following result is well known: Suppose that X ? is an ANR and X is a subspace of X ? . Then X is a strong (or stationary) deformation retract of X ? if and only if X is a deformation retract of X ? . In this paper, a[...]![]()
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The notions of quasidomination and quasi-equivalence of compacta were introduced by K. Borsuk [Fund. Math. 93 (1976), no. 3, 197–212. These relations are weaker than the relations of shape domination and shape equivalence. According to Borsuk th[...]![]()
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Laguna, V.F. ; Morón, Manuel A. ; Rodríguez Sanjurjo, José Manuel | Symposium of General Topology | 1990S. Godlewski [Fundam. Math. 114, 1-9 (1981; Zbl 0498.54016)] proved that if a metrizable space X is a mutational retract of X0 and X is an MANR (mutational absolute neighborhood retract), then every component of X is a mutational retract of a co[...]![]()
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We study the internal structure of the global attractor of a uniformly persistent flow. We show that the restriction of the flow to the global attractor has duality properties which can be expressed in terms of certain attractor-repeller decompo[...]![]()
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K. Borsuk [Fund. Math. 99 (1978), no. 1, 35–42] extended the classical notion of Lyusternik-Shnirelman category (briefly L-S category) to the theory of shape and thereby introduced a shape invariant coefficient for a compactum X . This was subse[...]![]()
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Sánchez Gabites, Jaime Jorge ; Rodríguez Sanjurjo, José Manuel | American Mathematical Society | 2007Suppose phi : M x R -> M is a continuous flow on a locally compact metrizable space M and K is an ( asymptotically stable) attractor. Let D =partial derivative A( K) be the boundary of the basin of attraction of K. In the present paper it will [...]![]()
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The author generalizes some results of Ball concerning the relationship between the shape of a locally compact metrizable space with compact components and the shape of its components. The following results are proved. Let X and Y be locally com[...]![]()
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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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Let X, Y be two compacta with Sh(X) = Sh (Y). Then, the spaces of components of X, Y are homeomorphic. This does not happen, in general, when X, Y are quasi-equivalent. In this paper we give a sufficient condition for the existence of a homeomor[...]![]()
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Given an approximate mapping f ? ={f k }:X?Y between compacta from the Hilbert cube [K. Borsuk, Fund. Math. 62 (1968), 223–254, the author associates with f ? a (u.s.c.) multivalued mapping F:X?Y . If F is single-valued, F and f ? induce [...]![]()
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This article is an exposition of several results concerning the theory of continuous dynamical systems, in which Topology plays a key role. We study homological and homotopical properties of attractors and isolated invariant compacta as well as [...]![]()
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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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The author treats shape properties which movable compacta and their nonmovable components inherit from their movable components. First he shows that shape morphisms of movable compacta are completely determined by their restrictions to movable c[...]![]()
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An upper semicontinuous multivalued map F:X?Y is said to be ? -small if the diameter of F(x) is less than ? for each x?X . F and G are ? -homotopic if there is an ? -small homotopy H:X×I?Y joining F and G . F:X×[0,?)?Y is a fine multival[...]![]()
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For compact metric spaces X , Y contained in a given compact AR Q , the authors consider the set A(X,Y) of all approximative maps (in the sense of K. Borsuk [same journal 62 (1968), 223–254]). On A(X,Y) they define a metric making A(X,Y) a c[...]![]()
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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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Sánchez Gabites, Jaime Jorge ; Rodríguez Sanjurjo, José Manuel | Croatian Mathematical Society; Department of Mathematics, University of Zagreb | 2007-06A compact stable attractor K of a continuous flow on a locally compact metric space is shape equivalent to a compact positively invariant neighbourhood P in its basin of attraction, the shape equivalence being induced by the inclusion map. In [...]![]()
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Giraldo, A. ; Rodríguez Sanjurjo, José Manuel | Society for Industrial and Applied Mathematics | 2009We study dynamical and topological properties of the singularities of continuations of attractors of flows on manifolds. Despite the fact that these singularities are not isolated invariant sets, they share many of the properties of attractors; [...]![]()
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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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In this paper the author studies homotopy properties of FANR spaces (fundamental absolute neighborhood retracts). The principal result is a theorem about homotopy extensions for fundamental ? -near sequences such that the initial and final level[...]![]()
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Laguna, V. F. ; Rodríguez Sanjurjo, José Manuel | Japanese Association of mathematical Sciences | 1986Let A(X,Y) be the set of all approximate maps ofa compactum X to a compactum Y. In this paper we define two topologies on A(X,Y) and study some properties of the spaces obtained.![]()
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The authors study the space $A\sp*(X,Y)$ of all approximative maps f\{f\sb k: X\to Y\}$ between compact subsets X, Y of the Hilbert cube. The topology of this space is given by the pseudometric $d\sp*(\underline f,\underline g)=\inf \{\sup \{d[...]![]()
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This paper is a survey on how topological techniques (mainly from algebraic and geometric topology) can be applied to the study of flows. The first five sections constitute a self-contained introduction to the subject, including the proofs of se[...]![]()
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In this interesting paper, the author gives a stability condition for the fixed point property in terms of K. Borsuk's fundamental metric on a hyperspace of a compact metric space. This condition is equivalent to that originally given by V. L. K[...]![]()
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This paper is a review of applications of shape theory to the theory of dynamical systems. The paper gives careful statements with references to other papers containing more details and proofs. There is a brief introduction to the theory of sha[...]![]()
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Summary (translated from the Spanish): "In this expository paper we present some relations between the two branches of mathematics mentioned in the title. In particular, we prove some cohomological properties of the non-saddle decomposition of a[...]![]()
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Nhu, Nguyen Tho ; Rodríguez Sanjurjo, José Manuel ; Van An, Tran | American Mathematical Society | 1997-10In this second part of our paper, we apply the result of Part 1 to show that the compact convex set with no extreme points, constructed by Roberts (1977), is an AR.![]()
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Morón, Manuel A. ; Sánchez Gabites, Jaime Jorge ; Rodríguez Sanjurjo, José Manuel | Polish acad sciences inst mathematics | 2007This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and[...]![]()
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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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We consider parameterized families of flows in locally compact metrizable spaces and give a characterization of those parameterized families of flows for which uniform persistence continues. On the other hand, we study the generalized Poincare-A[...]![]()
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We present sufficient conditions on an approximate mapping F : H --> Y of approximate inverse systems in order that the limit f : X --> Y of F is a universal map in the sense of Holsztynski. A similar theorem holds for a more restrictive conce[...]![]()
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We study dynamical and topological properties of the unstable manifold of isolated invariant compacta of flows. We show that some parts of the unstable manifold admit sections carrying a considerable amount of information. These sections enable [...]