Dynamical systems and shapes

作者: J. J. Sánchez-Gabites

DOI: 10.1007/BF03191815

关键词:

摘要: This survey is an introduction to some of the methods, techniques and concepts from algebraic topology related areas (homotopy theory, shape theory) which can be fruitfully applied study problems concerning continuous dynamical systems. To this end two instances exemplify interaction between dynamics are considered, namely, Conley’s index theory properties certain attractors.

参考文章(68)
Dietmar Salamon, CONNECTED SIMPLE SYSTEMS AND THE CONLEY INDEX OF ISOLATED INVARIANT SETS Transactions of the American Mathematical Society. ,vol. 291, pp. 1- 41 ,(1985) , 10.1090/S0002-9947-1985-0797044-3
Richard C Churchill, Isolated invariant sets in compact metric spaces Journal of Differential Equations. ,vol. 12, pp. 330- 352 ,(1972) , 10.1016/0022-0396(72)90036-8
J.M.R. Sanjurjo, On the Structure of Uniform Attractors Journal of Mathematical Analysis and Applications. ,vol. 192, pp. 519- 528 ,(1995) , 10.1006/JMAA.1995.1186
Bernd G{ünther, Jack Segal, Every attractor of a flow on a manifold has the shape of a finite polyhedron Proceedings of the American Mathematical Society. ,vol. 119, pp. 321- 329 ,(1993) , 10.1090/S0002-9939-1993-1170545-4
A. Giraldo, M.A. Morón, F.R. Ruiz Del Portal, J.M.R. Sanjurjo, Shape of global attractors in topological spaces Nonlinear Analysis-theory Methods & Applications. ,vol. 60, pp. 837- 847 ,(2005) , 10.1016/J.NA.2004.03.036
J. J. Sánchez-Gabites, J. M. R. Sanjurjo, On the topology of the boundary of a basin of attraction Proceedings of the American Mathematical Society. ,vol. 135, pp. 4087- 4098 ,(2007) , 10.1090/S0002-9939-07-08972-1
M.M. Peixoto, Structural stability on two-dimensional manifolds☆ Topology. ,vol. 1, pp. 101- 120 ,(1962) , 10.1016/0040-9383(65)90018-2
Ketty de Rezende, Smale flows on the three-sphere Transactions of the American Mathematical Society. ,vol. 303, pp. 283- 310 ,(1987) , 10.1090/S0002-9947-1987-0896023-7
Marston Morse, Relations between the critical points of a real function of $n$ independent variables Transactions of the American Mathematical Society. ,vol. 27, pp. 345- 396 ,(1925) , 10.1090/S0002-9947-1925-1501318-X