Existence of gibbs measures for countable Markov shifts

By O. Sarig. 2003

235 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/fbfcdf475e80c3ca28c09a7a5d7f8cafe6279b7d

How researchers see this paper

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

In Mathematical Physics

Citations in the corpus

Diffusion for chaotic plane sections of 3-periodic surfaces (2014, background): “nsiderthepotential˚= r;whereristherooffunction. ThenfortheMarkovmapTdeﬁnedoftheRauzygasketthereexistsaninvariant equilibriummeasure,andthismeasureisunique. Proof. In accordance with Corollary 2 from [Sa03] our potential ˚is positive recurrent (see [Sa03] for precise terminology) and there exist >”
Multifractal analysis of Birkhoff averages for countable Markov maps (2010, result): “This notion of pressure satisfies the following results (see [21, 26, 27, 28]),”
Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps (2003, background): “Unfortunately, if |S| = ∞ this never happens, unless A satisfies the BIP property (see [18] and [26] for statements and definitions), so the general case cannot be treated this way.”
Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts (2009, background): “In both cases the underlying CMS must satisfy a certain combinatorial condition (the big images and preimages (BIP) property [ S3 ]).”
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].”
Equilibrium states for non-uniformly expanding maps (2003, background): “Several authors have been studying equilibrium states for non-hyperbolic systems: Bruin, Keller [BK98] and Denker, Urbanski [DU92, Urb98], for interval maps and rational functions on the sphere, and Buzzi, Maume, Sarig [Buz99, BMD02, BS, Sar03 ] and Yuri [Yur99, Yur00, Yur03], for countable Markov ”
Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps (2008, unknown): “Buzzi, Sarig [BS03, Sar99, Sar01, Sar03 , Yur03] for countable Markov shifts.”
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”
Equilibrium States for Interval Maps: Potentials with sup φ − inf φ < htop(f) (2007, methodology): “…1 of [Sa1] implies that if ϕ has summable variations then for any C , Although we do not assume that the potential ϕ has summable variations, it is important that the induced potential Φ has summable variations, as we want to apply the following result which collects the main theorems of [Sa3].”
Fourier transforms of Gibbs measures for the Gauss map (2013, methodology): “The fact that the Gauss map is conjugate to the full shift on NN enables us to use the thermodynamical formalism for countable shifts developed by Mauldin and Urbański in [24] and Sarig in the papers [31, 32].”