Continuum-wise expansiveness and specification for set-valued functions and topological entropy
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- by Welington Cordeiro and Maria José Pacífico PDF
- Proc. Amer. Math. Soc. 144 (2016), 4261-4271 Request permission
Abstract:
We define the concept of continuum-wise expansiveness for set-valued functions. We prove that for a compact metric space $X$ with positive topological dimension, if a set-valued function is $cw$-expansive, then its topological entropy is positive. We also introduce the notion of point-wise specification property for set-valued functions and prove that set-valued functions with this property have positive entropy.References
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Additional Information
- Welington Cordeiro
- Affiliation: Department of Mathematics, The Pennsylvania State University, State College, Pennsylvania 16802
- MR Author ID: 1027592
- Email: wud11@psu.edu
- Maria José Pacífico
- Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530 CEP 21.945-970, Rio de Janeiro, RJ, Brazil
- MR Author ID: 196844
- Email: pacifico@im.ufrj.br
- Received by editor(s): October 26, 2015
- Published electronically: June 17, 2016
- Additional Notes: The first author was partially supported by CNPq
The second author was partially supported by CNPq, PRONEX-Dyn.Syst., FAPERJ - Communicated by: Nimish A. Shah
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4261-4271
- MSC (2010): Primary 37A35, 37B40, 37D45, 54C60
- DOI: https://doi.org/10.1090/proc/13168
- MathSciNet review: 3531177