Dinámica colectiva

HÉCTOR MÉNDEZ LANGO^*

UNAM, Facultad de Ciencias, Departamento de Matemáticas, Ciudad Universitaria,
C.P. 04510, D.F., México.

Resumen. Dado un espacio métrico compacto X y una función continua ƒ : X → X, consideramos el hiperespacio de todos los subconjuntos de X que son cerrados y no vacíos, 2^X, con la métrica de Hausdorff, y la función que induce ƒ en él, : 2^X → 2^X. En la última década ha habido una importante cantidad de artículos estudiando las relaciones entre las propiedades dinámicas de ƒ y las de . En este trabajo presentamos un panorama con varios de los resultados más importantes. Ofrecemos, además, una breve colección de varias de las conjeturas y preguntas abiertas que se han planteado en esta área.

Palabras Claves: Hiperespacio, dinámica discreta, dinámica colectiva, entropía.
MSC2010: 54B20, 54C05, 54C70.

Collective dynamics

Abstract. For a metric compact set X and a continuous map f : X → X we consider the hyperspace 2^X of all closed and nonempty subsets of X with the Hausdorff metric, and the induced map : 2^X → 2^X. In the past few years the study of the connection between the dynamical properties of ƒ and those of has became an important and fruitful topic. In this paper we survey some significant results in this area. Also we collect some open questions and conjectures.

Keywords: Hyperspace, discrete dynamics, collective dynamics, entropy.

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^*E-mail : hml@ciencias.unam.mx
Recibido: 2 de abril de 2012, Aceptado: 31 de mayo de 2012.