On the dynamics of the induced map in the hyperspace of subcontinua
by
Hector Mendez Lango
Facultad de Ciencias, UNAM
Coauthors: Gerardo Acosta, Alejandro Illanes

Let f be a continuous self-map of a continuum X. Let C(f) be the map induced by f in the space of all subcontinua of X, C(X). The aim of this talk is to produce a dendrite X and a self-homeomorphism of X, say f, such that for each x in X the omega limit set of x under f consists of just one point (thus the dynamics of f is very simple) and, despite of that, to show the existence of an element of C(X), say A, such that the omega limit set of A under C(f) is homeomorphic to the Hilbert Cube (thus the dynamics of C(f) is not that simple).

Date received: April 26, 2007