The entropy theory of symbolic extensions

By Mike Boyle, Tomasz Downarowicz. 2004

127 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/eaec316ddb52b7aa8aed0667f4436f1b6dd35cb2

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In Mathematical Physics

Citations in the corpus

Variational principles for topological entropies of subsets (2010, background): “152–153 in [5]), we associate to this sequence a zero-dimensional principal extension (Z,R) of (X × Y,T × S) with R invertible.”
A local variational principle of pressure and its applications to equilibrium states (2007, background): “Another characterization of asymptotically h-expansivity is recently given by Boyle and Downarowicz [5] as the following: (X,T ) is asymptotically h-expansive iff it has a principal extension to a symbolic system.”
Symbolic extensions and smooth dynamical systems (2005, methodology): “Thus, the essential sequence A of partitions for f gives us a non-decreasing sequence of uppersemicontinuous functions with uppersemicontinuous differences H def = {hk} on M( f ) as studied in [2].”
Topological chaos: what may this mean? (2008, background): “For instance any 0-entropy system (X, f ) has a 0-entropy symbolic extension, which is sensitive except in trivial cases while obviously strongly related to (X, f ) [17].”
Entropy in dynamical systems (2003, methodology): “This is why we replicate from [Boyle and Downarowicz, 2004] two explicit zero-dimensional examples in the form of symbolic array systems.”
Local Entropy Theory of a Random Dynamical System (2011, background): “me measure-theoretic entropy for all invariant Borel probability measures of the system. This plays an important role in the study of relative entropy theory and entropy theory of symbolic extensions [11]. Based on the same ideas, we can introduce a similar concept in our setting. Let the family Fi ”
The Entropy Conjecture for Diffeomorphisms away from Tangencies (2010, result): “This is in contrast with previous work of Downarwicz, Newhouse [12], based on the theory developed by Boyle, Downarwicz [5], where it is shown that nonexistence of symbolic extensions is typical on the closure of the set of area preserving diffeomorphisms with homoclinic tangencies.”