On the Dynamics of Induced Maps on the Space of Probability Measures

Abstract

For the generic continuous map and for the generic homeomorphism of the Cantor space, we study the dynamics of the induced map on the space of probability measures, with emphasis on the notions of Li-Yorke chaos, topological entropy, equicontinuity, chain continuity, chain mixing, shadowing and recurrence. We also establish some results concerning induced maps that hold on arbitrary compact metric spaces.

23 pages

References in corpus (1)

• Graph Theoretic Structure of Maps of the Cantor Space

Cited by in corpus (3)

• Topological dynamics of Zadeh's extension on the space of upper semi-continuous fuzzy sets
• Uniformly Positive Entropy of Induced Transformations
• Dynamics of continuous maps induced on the space of probability measures