Biblioteca de la Universidad Complutense de Madrid

Topological robustness of non-saddle sets

Impacto

Giraldo, A. y Rodríguez Sanjurjo, José Manuel (2009) Topological robustness of non-saddle sets. Topology and its Applications, 156 (11). pp. 1929-1936. ISSN 0166-8641

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

212kB

URL Oficial: http://www.sciencedirect.com/science/article/pii/S0166864109000868




Resumen

We study in this paper preservation of dynamical and shape theoretical properties under Continuation for parametrized families of flows. We show that, although attractors continue. the same does not hold for non-saddle sets. However, when they continue, their shape is preserved in quite general settings, which include differentiable families of flows and regular non-saddle sets for general flows, not necessarily differentiable. We also Study how the continuation of a non-saddle set influences that of its dual non-saddle set.


Tipo de documento:Artículo
Información Adicional:

Conference on General Topology in Honour of Peter Collins and Mike Reed, AUG 07-10, 2006, Oxford, ENGLAND

Palabras clave:Shape equivalence, Dynamical system, Isolated invariant set, Continuation of non-saddle sets
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID:16730
Referencias:

A. Beck, On invariant sets, Ann. of Math. (2) 67 (1958) 99–103.

N.P. Bhatia, G.P. Szego, Stability Theory of Dynamical Systems, Grundlehren Math. Wiss., vol. 161, Springer-Verlag, Berlin, 1970.

S.A. Bogatyi, V.I. Gutsu, On the structure of attracting compacta, Differ. Urav. 25 (1989) 907–909 (in Russian).

K. Borsuk, Theory of Shape, Monogr. Mat., vol. 59, Polish Scientific Publishers, Warszawa, 1975.

C.C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. Math., vol. 38, Amer. Math. Soc., Providence, RI, 1976.

C.C. Conley, The gradient structure of a flow, Ergodic Theory Dynam. Systems 8∗ (1988) 11–26.

C.C. Conley, R.W. Easton, Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc. 158 (1971) 35–61.

J.M. Cordier, T. Porter, Shape Theory. Categorical Methods of Approximation, Ellis Horwood Ser. Math. Appl., Ellis Horwood Ltd, Chichester, 1989.

J. Dydak, J. Segal, Shape Theory: An Introduction, Lecture Notes in Math., vol. 688, Springer-Verlag, Berlin, 1978.

R.W. Easton, Geometric Methods for Discrete Dynamical Systems, Oxford Engrg. Sci. Ser., vol. 50, Oxford University Press, New York, 1998.

S. Eilenberg, N. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, 1952.

A. Giraldo, J.M.R. Sanjurjo, On the global structure of invariant regions of flows with asymptotically stable attractors, Math. Z. 232 (1999) 739–746.

A. Giraldo, M.A. Morón, F.R. Ruíz del Portal, J.M.R. Sanjurjo, Some duality properties of non-saddle sets, Topology Appl. 113 (2001) 51–59.

B. Günther, 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.

S. Mardešic, Strong Shape and Homology, Springer Monogr. Math., Springer, Berlin, 2000.

S. Mardešic, J. Segal, Shape Theory, North-Holland, Amsterdam, 1982.

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, An intrinsic description of shape, Trans. Amer. Math. Soc. 329 (1992) 625–636.

J.M.R. Sanjurjo, Multihomotopy, Cech 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.

J.M.R. Sanjurjo, Lusternik–Schnirelmann category and Morse decompositions, Mathematika 47 (2000) 299–305.

J.M.R. Sanjurjo, Morse equations and unstable manifolds of isolated invariant sets, Nonlinearity 16 (2003) 1435–1448.

Depositado:16 Oct 2012 09:31
Última Modificación:07 Feb 2014 09:34

Sólo personal del repositorio: página de control del artículo