Combined Dynamics on Hyperspaces

CCNY Dynamical Systems Seminar

Time and place

1 PM on Tuesday, November 23rd, 2010; NAC 6-113

Anima Nagar (Indian Institute of Technology)

Abstract

A continuous map on a topological space, induces a continuous map on its hyperspace (space of closed/compact subsets) given a suitable hyperspace topology. We consider the general HIT & MISS topology on the hyperspace, and discuss the conditions under which the dynamics displayed by the base map can be inherited by the induced map on the hyperspace and vice versa. We further consider the same when a combined effect of the join of distinct maps (relations) induces a map on the hyperspace. We propose various problems that result from such a study.