On the Dynamics of Induced Maps on the Space of Probability Measures
Dynamical Systems
2023-05-09 v1 Probability
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.
Keywords
Cite
@article{arxiv.1409.1478,
title = {On the Dynamics of Induced Maps on the Space of Probability Measures},
author = {Nilson C. Bernardes and Rômulo M. Vermersch},
journal= {arXiv preprint arXiv:1409.1478},
year = {2023}
}
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23 pages