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.References
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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
- MR Author ID: 344182
- 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
- Received by editor(s): August 17, 2014
- Received by editor(s) in revised form: October 26, 2014
- Published electronically: January 6, 2016
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3546780