Geodesic
Logarithmic expansion, entropy, and dimension for set-valued maps
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Optimal control, Tome 178 (2020), pp. 31-40

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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
Mots-clés : dimension. 
@article{INTO_2020_178_a2,
     author = {D. Carrasco-Olivera and R. Metzger and C. Morales},
     title = {Logarithmic expansion, entropy, and dimension for set-valued maps},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {31--40},
     publisher = {mathdoc},
     volume = {178},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_178_a2/}
}
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D. Carrasco-Olivera; R. Metzger; C. Morales. Logarithmic expansion, entropy, and dimension for set-valued maps. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Optimal control, Tome 178 (2020), pp. 31-40. http://geodesic.mathdoc.fr/item/INTO_2020_178_a2/