Sánchez Gabites, Jaime Jorge and Rodríguez Sanjurjo, José Manuel (2008) Multivalued maps, selections and dynamical systems. Topology and its Applications, 155 (8). pp. 874-882. ISSN 0166-8641
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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 dynamical concepts such as stability or attraction can be easily characterized in terms of Psi and moreover, the classical result that an attractor in R '' has the shape of a finite polyhedron can be reinforced under the hypotheses that the mapping Psi is small and has a selection.
|Uncontrolled Keywords:||Multivaluedmaps; Selections; Upper semifinite topology; Dynamicalsystems; Attractors|
|Subjects:||Sciences > Mathematics > Geometry|
Sciences > Mathematics > Topology
N.P. Bhatia, G.P. Szegö, Stability Theory of Dynamical Systems, Die Grundlehren der mathematischen Wissenschaften, Band161, Springer-Verlag, 1970.
S.A. Bogatyı, Approximative and fundamental retracts, Mat. Sb. (N.S.) 93 (135) (1974) 90–102.
S.A. Bogaty˘ı, V.I. Gutsu, On the structure of attracting compacta, Differentsialnye Uravneniya 25 (5) (1989) 907–909, 920.
K. Borsuk, Theory of Retracts, Monografie Matematyczne, vol. 44, Pa´nstwowe Wydawnictwo Naukowe, 1967.
K. Borsuk, On movable compacta, Fund. Math. 66 (1969/1970) 137–146.
K. Borsuk, Theory of Shape, Monografie Matematyczne, vol. 59, Pa´nstwowe Wydawnictwo Naukowe, 1975.
J. Dydak, On internally movable compacta, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1) (1979) 107–110.
J. Dydak, J. Segal, Shape Theory. An Introduction, Lecture Notes in Mathematics, vol. 688, Springer, 1978.
A. Giraldo, M.A. Morón, F.R. Ruiz del Portal, J.M.R. Sanjurjo, Shape of global attractors in topological spaces, Nonlinear Anal. 60 (5) (2005) 837–847.
B. Günther, J. Segal, Every attractor of a flow on a manifold has the shape of a finite polyhedron, Proc. Amer. Math. Soc. 119 (1) (1993) 321–329.
S. Hu, Theory of Retracts, Wayne State University Press, 1965.
A. Illanes, S.B. Nadler Jr., Hyperspaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 216, Marcel Dekker, Inc., 1999.
V.F. Laguna, J.M.R. Sanjurjo, Internal fundamental sequences and approximative retracts, Topology Appl. 17 (2) (1984) 189–197.
S. Mardešic, J. Segal, Shape Theory. The Inverse System Approach, North-Holland Mathematical Library, vol. 26, North-Holland, 1982.
E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1) (1951) 152–182.
D. Repovs, P.V. Semënov, E. Michael’s theory of continuous selections. Development and applications, Russian Math. Surveys 49 (6) (1994) 157–196.
D. Repovs, P.V. Semënov, Continuous Selections of Multivalued Mappings, Mathematics and its Applications, vol. 455, Kluwer Academic Publishers, 1998.
D. Repovs, P.V. Semënov, Continuous Selections of Multivalued Mappings, Recent Progress in General Topology, II, North-Holland, 2002.
D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc. 291 (1) (1985) 1–41.
J.M.R. Sanjurjo, Selections of multivalued maps and shape domination, Math. Proc. Cambridge Philos. Soc. 107 (3) (1990) 493–499.
J.M.R. Sanjurjo, Multihomotopy, Cˇ ech spaces of loops and shape groups, Proc. London Math. Soc. (3) 69 (2) (1994) 330–344.
J.M.R. Sanjurjo, On the structure of uniform attractors, J. Math. Anal. Appl. 192 (2) (1995) 519–528.
J.E. West, Mapping Hilbert cube manifolds to ANR’s: a solution of a conjecture of Borsuk, Ann. of Math. (2) 106 (1977) 1–18.
|Deposited On:||19 Oct 2012 11:09|
|Last Modified:||19 Oct 2012 11:09|
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