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Continuum-wise expansiveness and specification for set-valued functions and topological entropy


Authors: Welington Cordeiro and Maria José Pacífico
Journal: Proc. Amer. Math. Soc. 144 (2016), 4261-4271
MSC (2010): Primary 37A35, 37B40, 37D45, 54C60
DOI: https://doi.org/10.1090/proc/13168
Published electronically: June 17, 2016
MathSciNet review: 3531177
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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.


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Additional Information

Welington Cordeiro
Affiliation: Department of Mathematics, The Pennsylvania State University, State College, Pennsylvania 16802
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
Email: pacifico@im.ufrj.br

DOI: https://doi.org/10.1090/proc/13168
Keywords: Continuum-wise expansiveness, set-valued functions, entropy, specification property
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
Article copyright: © Copyright 2016 American Mathematical Society

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