Lusternik-Schnirelmann category and Morse decompositions
| dc.contributor.author | Rodríguez Sanjurjo, José Manuel | |
| dc.date.accessioned | 2023-06-20T18:46:15Z | |
| dc.date.available | 2023-06-20T18:46:15Z | |
| dc.date.issued | 2000-12 | |
| dc.description.abstract | 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 case of ANR's (Absolute Neighbourhood Retracts). We refer to the review articles [10] by R. H. Fox and [15, 16] by I. M. James for general information about this topological invariant. We shall use in this paper the definition of the Lusternik-Schnirelmann category of a compactum introduced by K. Borsuk in [4] | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21823 | |
| dc.identifier.doi | 10.1112/S0025579300015904 | |
| dc.identifier.issn | 0025-5793 | |
| dc.identifier.officialurl | http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7015084 | |
| dc.identifier.relatedurl | http://journals.cambridge.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58564 | |
| dc.issue.number | 1-2 | |
| dc.journal.title | Mathematika. A Journal of Pure and Applied Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 305 | |
| dc.page.initial | 299 | |
| dc.publisher | Cambridge Univ. Press | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.164 | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Lusternik-Schnirelmann category and Morse decompositions | |
| dc.type | journal article | |
| dc.volume.number | 47 | |
| dcterms.references | N. P. Bhatia. Attraction and nonsaddle sets in dynamical systems. J. Differential Equations, 8 (1970), 229–249. N. P. Bhatia and G. P. Szego. Stability Theory of Dynamical Systems (Springer, Berlin, 1970). K. Borsuk. Theory of Shape, Monografie Matematyczne 59, Warszawa, 1975. K. Borsuk. On the Lusternik–Schnirelmann category in the theory of shape. Fund. Math., 99 (1978), 35–42. M. L. Cartwright and J. E. Littlewood. Some fixed point theorems. Ann. Math., 54 (1951), 1–37. C. C. Conley. Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. in Math., 38 (Amer. Math. Soc., Providence, R.I., 1976). C. C. Conley and E. Zehnder. The Birkhoff–Lewis Fixed Point Theorem and a conjecture of V. I. Arnold. Inventiones Math., (1983), 33–49. J. M. Cordier and T. Porter. Shape Theory. Categorical Methods of Approximation, Ellis Horwood Series: Mathematics and its Applications, Chichester, 1989. J. Dydak and J. Segal. Shape Theory: An Introduction, Lecture Notes in Math. 688, (Springer-Verlag, Berlin, 1978). R. H. Fox. On the Lusternik–Schnirelmann category. Ann. Math. 42 (1941), 333–370. A. Giraldo and J. M. R. Sanjurjo. On the global structure of invariant regions of flows with asymptotically stable attractors, Math. Zeitschrift, to appear. B. Günther and J. Segal. Every attractor of a flow on a manifold has the shape of a finite polyhedron. Proc. Amer. Math. Soc., 119 (1993), 321–329. H. M. Hastings. Shape theory and dynamical systems. In eds. N. G. Markley and W. Perizzo: The Structure of Attractors in Dynamical Systems, Lecture Notes in Math. 668 (Springer-Verlag, Berlin 1978), 150–160. S. T. Hu. Theory of Retracts (Wayne State University Press, Detroit, 1967). I. M. James. On category in the sense of Lusternik–Schnirelmann, Topology 17 (1978), 331–348. I. M. James. Lusternik–Schnirelmann category. In Handbook of Algebraic Topology (Elsevier, 1995), 1293–1310. S. Mardešić and J. Segal. Shape Theory (North Holland, Amsterdam, 1982). M. Pozniak. Lusternik–Schnirelmann category of an isolated invariant set. Univ. Iagellonicae Acta Math., 31 (1994), 129–139. J. W. Robbin and D. Salamon. Dynamical systems, shape theory and the Conley index. Ergod. Th. and Dynam. Sys., 8* (1998), 375–393. D. Salamon. Connected simple systems and the Conley index of isolated invariant sets. Trans. Amer. Math. Soc., 291 (1985), 1–41. J. M. R. Sanjurjo. Multihomotopy, Čech. spaces of loops and shape groups. Proc. London Math. Soc., 69 (1994), 330–344. J. M. R. Sanjurjo. On the structure of uniform attractors. J. Math. Anal. Appl., 192 (1995), 519–528. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f54f1d9d-37e9-4c15-9d97-e34a6343e575 | |
| relation.isAuthorOfPublication.latestForDiscovery | f54f1d9d-37e9-4c15-9d97-e34a6343e575 |
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