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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 178, Pages 31–40
DOI: https://doi.org/10.36535/0233-6723-2020-178-31-40 (Mi into610) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Logarithmic expansion, entropy, and dimension for set-valued maps

D. Carrasco-Oliveraa, R. Metzgerb, C. Moralesc

a Universidad del Bío-Bío
b Universidad Nacional de Ingenieria, Lima, Peru
c Universidade do Estado do Rio de Janeiro
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DOI: https://doi.org/10.36535/0233-6723-2020-178-31-40
Abstract: We obtain a lower bound for the entropy of a (not necessarily invariant) Borel probability measure with respect to an upper semicontinuous set-valued map as the product of the lower dimension of the measure and the logarithmic expansion rate. This is a generalization of the well-known measure-preserving single-valued case.
Keywords: logarithm expansion, metric entropy, dimension.
Funding agency Grant number
Comisión Nacional de Investigación Científica y Tecnológica 1181061
National Council for Scientific and Technological Development (CNPq) MATH05-ERGOPTIM
The work of D. Carrasco-Olivera was supported by the FONDECYT 1181061 project, CONICYT (Chile). The work of R. Metzger was supported by the Pos-Doutorado Verano 2015 project, IMPA, Rio de Janeiro, Brazil. The work of S. A. Morales was supported by projects CNPq-Brazil and MATHAMSUB 15 MATH05-ERGOPTIM.
Document Type: Article
UDC: 517.938
MSC: 37D40, 54C60
Language: Russian
Citation: D. Carrasco-Olivera, R. Metzger, C. Morales, “Logarithmic expansion, entropy, and dimension for set-valued maps”, Optimal control, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 178, VINITI, Moscow, 2020, 31–40
Citation in format AMSBIB
\Bibitem{CarMetMor20}
\by D.~Carrasco-Olivera, R.~Metzger, C.~Morales
\paper Logarithmic expansion, entropy, and dimension for set-valued maps
\inbook Optimal control
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 178
\pages 31--40
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into610}
\crossref{https://doi.org/10.36535/0233-6723-2020-178-31-40}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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