Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps

By Jérôme Buzzi, O. Sarig. Ergodic Theory and Dynamical Systems, 2003

189 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c5defbda9734827a9052bec468fa942b3e029f7f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Yakov Pesin
2. Van Cyr
3. Vilton Pinheiro
4. Jérôme Buzzi
5. O. Sarig
6. S. Senti
7. Vitor Araujo
8. Maria José Pacifico

In Mathematical Physics

1. Vilton Pinheiro
2. Jérôme Buzzi
3. Van Cyr
4. O. Sarig
5. Mike Boyle
6. Ricardo Gómez
7. Yakov Pesin
8. S. Senti

Citations in the corpus

• Measures of maximal entropy for surface diffeomorphisms (2018, unknown): “As Σ is transitive and φ ◦ π is Hölder-continuous, [37] implies that μ̂ = ν̂, hence μ = ν, proving the first property of Corollary 3.”
• Expanding Measures (2008, background): “Future applications Recently there was an increasing development of the study of the thermodynamic formalism beyond the uniformly hyperbolic context (including countable Markov shift) by several authors (this list is certainly not complete): Araujo [7], Arbieto, Matheus, Oliveira, Varandas, Viana [8”
• Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts (2009, methodology): “then mφ is an equilibrium measure for φ .B y [ BS ], there is at most one such measure, so mφ is unique.”
• Large Deviations for Non-Uniformly Expanding Maps (2006, background): “kov partitions with infinitely many symbols leading to a thermodynamical formalism of gases with infinitely many 4 V. ARAUJO AND M. J. PACIFICO´ states, a hard subject not yet well understood (see e.g. [23, 10] for recent developments). Assuming conditions NUE or PHNUE we are able to extend some of th”
• Equilibrium measures for maps with inducing schemes (2006, background): “Various versions of these results were obtained by Mauldin and Urbański [23], by Sarig [31, 32, 34] and by Yuri [46] (see also [1] and [12]).”
• Almost isomorphism for countable state Markov shifts (2004, background): “One motivation of our paper is recent interest in the thermodynamic formalism for countable state Markov shifts [11, 18, 23, 24, 25, 39, 49, 50, 51, 53].”