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


Authors: Nilson C. Bernardes Jr. and Rômulo M. Vermersch
Journal: Trans. Amer. Math. Soc. 368 (2016), 7703-7725
MSC (2010): Primary 37B99, 54H20; Secondary 54E52, 60B10, 28A33
DOI: https://doi.org/10.1090/tran/6615
Published electronically: January 6, 2016
MathSciNet review: 3546780
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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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Additional Information

Nilson C. Bernardes Jr.
Affiliation: Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ, 21945-970, Brasil
Email: ncbernardesjr@gmail.com

Rômulo M. Vermersch
Affiliation: Departamento de Tecnologias e Linguagens, Instituto Multidisciplinar, Universidade Federal Rural do Rio de Janeiro, Av. Governador Roberto Silveira s/n, Nova Iguaçu, RJ, 26020-740, Brasil
Address at time of publication: Departamento de Matemática, Centro de Física e Matemática, Universidade Federal de Santa Catarina, Florianópolis, SC, 88040-900, Brasil
Email: romulo.vermersch@gmail.com, romulo.vermersch@ufsc.br

DOI: https://doi.org/10.1090/tran/6615
Keywords: Cantor space, continuous maps, homeomorphisms, probability measures, Prohorov metric, dynamics
Received by editor(s): August 17, 2014
Received by editor(s) in revised form: October 26, 2014
Published electronically: January 6, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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