Fixed point index in hyperspaces: A Conley-type index for discrete semidynamical systems.
| dc.contributor.author | Romero Ruiz del Portal, Francisco | |
| dc.contributor.author | Salazar, J. M. | |
| dc.date.accessioned | 2023-06-20T17:10:46Z | |
| dc.date.available | 2023-06-20T17:10:46Z | |
| dc.date.issued | 2001 | |
| dc.description.abstract | 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 hyperspace of X. For any compact isolated invariant set, K subset of U, this fixed point index produces, in a very natural way, a Conley-type (integer valued) index for K. This index is computed and it is shown that it only depends on what is called the attracting part of K. The index is used to obtain a characterization of isolating neighbourhoods of compact invariant sets with non-empty attracting part. This index also provides a characterization of compact isolated minimal sets that are attractors | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/19894 | |
| dc.identifier.doi | 10.1017/S0024610701002162 | |
| dc.identifier.issn | 0024-6107 | |
| dc.identifier.officialurl | http://jlms.oxfordjournals.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57899 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of the London Mathematical Society. Second Series | |
| dc.language.iso | eng | |
| dc.page.final | 204 | |
| dc.page.initial | 191 | |
| dc.publisher | Oxford University Press | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | Fixed point index | |
| dc.subject.keyword | Hyperspaces | |
| dc.subject.keyword | Attractors | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Fixed point index in hyperspaces: A Conley-type index for discrete semidynamical systems. | |
| dc.type | journal article | |
| dc.volume.number | 64 | |
| dcterms.references | N. P. Bhatia and G. P. Szego , Stability theory of dynamical systems (Springer, Berlin, 1970). K. Borsuk, Theory of retracts, Monografie Matematyczne 44 (PWN, Warsaw, 1967). R. F. Brown, The Lefschetz fixed point theorem (Scott,Foresman, Glenview, IL, 1971). C. C. Conley, `Isolated invariant sets and the Morse index', CBMS 38 (American Mathematical Society, Providence, RI, 1978). D. W. Curtis and R. M. Schori, `2X and C(X) are homeomorphic to the Hilbert cube', Bull. Amer.Math. Soc. 80 (1974) 927-931. D. W. Curtis, `Hyperspaces of noncompact metric spaces',Compositio Math. 40 (1980) 139-152. A. Dold, `Fixed point index and fixed point theorem for Euclidean neighbourhood retracts ',Topology 4 (1965) 1-8. J. Girolo, `Approximating compact sets in normed linear spaces', Pacific J. Math. 98 (1992)81-89. 9. M. Gobbino and M. Sardella, `On the connectedness of attractors for dynamical systems',J. Differential Equations 133 (1997) 1-14. S. T. Hu, Theory of retracts (Wayne State University Press, Detroit, 1965). T. Kaczynski and M. Mrozek, `Stable index pairs for discrete dynamical systems', Canad. Math.Bull. 40 (1997) 448-455. M. Mrozek, `Index pairs and the fixed point index for semidynamical systems with discrete time',Fund. Math. 133 (1989) 179-194. M. Mrozek, `Leray functor and cohomological Conley index for discrete dynamical systems', Trans.Amer. Math. Soc. 318 (1990) 149-178. M. Mrozek, `Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces', Fund. Math. 145 (1994) 15-37. M. Mrozek and K. P. Rybakowski, `A cohomological Conley index for maps on metric spaces',J. Differential Equations 90 (1991) 143-171. N. T. Nhu, `Investigating the ANR-property of metric spaces', Fund. Math. 124 (1984) 243-254. R. D. Nussbaum, `Generalizing the fixed point index', Math. Ann. 228 (1977) 259-278. R. D. Nussbaum, `The fixed point index and some applications', Se!minaire de Mathe!matiques Supe!rieures (Presses de l'Universite! de Montreal, 1985). J. W. Robbin and D. Salamon, `Dynamical systems, shape theory and the Conley index', Ergodic Theory Dynam. Systems 8 (1988) 375-393. F. R. Ruiz del Portal and J. M. Salazar, `Shape index in metric spaces', preprint. E. Spanier, Algebraic topology (McGraw±Hill, New York,1966). H. Steinlein, `Uber die verallgemeinerten Fixpunktindizes von Iterierten verdichtender Abbildungen', Manuscripta Math. 8 (1973) 252-266. A. Szymczak, `The Conley index and symbolic dynamics',Topology 35 (1996) 287-299. J. E. West, `Mapping Hilbert cube manifolds to ANRs: a solution of a conjecture of Borsuk', Ann.of Math. 106 (1977) 1-18. | |
| dspace.entity.type | Publication |
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