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Continuum-wise expansiveness and specification for set-valued functions and topological entropy
- Source :
- Proceedings of the American Mathematical Society. 144:4261-4271
- Publication Year :
- 2016
- Publisher :
- American Mathematical Society (AMS), 2016.
-
Abstract
- We define the concept of continuum-wise expansiveness for set-valued functions. We prove that for a compact metric space X X with positive topological dimension, if a set-valued function is c w 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.
- Subjects :
- Discrete mathematics
Pointwise
Applied Mathematics
General Mathematics
Dynamical Systems (math.DS)
Topological entropy
37A35, 37B40, 37D45, 54C60
Topological entropy in physics
Binary entropy function
Positive entropy
Compact space
FOS: Mathematics
Mathematics - Dynamical Systems
Expansive
Mathematics
Subjects
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 144
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....fbb228a7ff2746fb4852a15cca2e820b