Symbolic extensions for nonuniformly entropy expanding maps
Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 129-151
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
A nonuniformly entropy expanding map is any $\mathcal{C}^1$ map defined on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a $\mathcal{C}^r$ nonuniformly entropy expanding map $T$ with $r>1$ has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T. Downarowicz and A. Maass [Invent. Math. 176 (2009)].
Keywords:
nonuniformly entropy expanding map mathcal map defined compact manifold whose ergodic measures positive entropy have only nonnegative lyapunov exponents prove mathcal nonuniformly entropy expanding map has symbolic extension explicit upper bound symbolic extension entropy terms positive lyapunov exponents following approach nbsp downarowicz nbsp maass invent math
Affiliations des auteurs :
David Burguet 1
@article{10_4064_cm121_1_12,
author = {David Burguet},
title = {Symbolic extensions for nonuniformly entropy expanding maps},
journal = {Colloquium Mathematicum},
pages = {129--151},
year = {2010},
volume = {121},
number = {1},
doi = {10.4064/cm121-1-12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm121-1-12/}
}
David Burguet. Symbolic extensions for nonuniformly entropy expanding maps. Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 129-151. doi: 10.4064/cm121-1-12
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