Teoría de la forma y sistemas dinámicos

Abstract

This paper is a review of applications of shape theory to the theory of dynamical systems. The paper gives careful statements with references to other papers containing more details and proofs. There is a brief introduction to the theory of shape as first proposed by K. Borsuk [Fund. Math. 62 (1968), 223–254. The relationship between the shape category and the homotopy category is discussed. The second section deals with the basic notions in dynamical systems. The paper deals primarily with continuous dynamical systems or flows. The third section deals with the shape of attractors of a dynamical system and how the neighborhood of attraction determines the shape. The fourth section deals with non-saddle isolated compacta showing that shape theory also restricts which compacta can be non-saddle isolated. Lastly, the fifth section deals with with the Lyusternik-Shnirelʹman category applied to isolated invariant sets. There is a helpful bibliography.