On the dynamics of induced maps on the space of probability measures

Bernardes, Nilson, Jr.; Vermersch, Rômulo

doi:10.1090/tran/6615

On the dynamics of induced maps on the space of probability measures
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by Nilson C. Bernardes Jr. and Rômulo M. Vermersch PDF

Trans. Amer. Math. Soc. 368 (2016), 7703-7725 Request permission

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.

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