Le théorème d’Ornstein (1970) est un des sommets de la théorie ergodique. C’est l’aboutissement des recherches initiées par Kolmogorov sur la classification des schémas de Bernoulli et le point de départ de résultats très généraux. Downarowicz et Serafin ont publié une élégante preuve de ce théorème difficile. Rappelons l’énoncé du théorème (dans sa version la [...]
Posts Tagged ‘ergodic theory’
Une courte preuve du théorème d’Ornstein par Downarowicz et Serafin
Posted in papers, tagged classification, entropy, ergodic theory on May 20, 2012 | Leave a Comment »
Renaud Leplaideur: Renormalisation des potentiels et transitions de phase
Posted in Dynamics, talks, tagged Dynamics, ergodic theory, mathematical physics, symbolic dynamics, thermodynamical formalism on September 28, 2010 | Leave a Comment »
Renaud Leplaideur a exposé au groupe de travail de théorie ergodique ses tout derniers travaux avec H. Bruin, A.T. Baraviera et A.O. Lopes. Ils ont en particulier construit, pour tout , une application de classe présentant une transition de phase et un compact , invariant, uniquement ergodique et indifférent: (i) ; (ii) ; (iii) le [...]
Alpern genericity theorem
Posted in Dynamics, papers, tagged Dynamics, ergodic theory, genericity, topological dynamics on January 27, 2010 | Leave a Comment »
Frédéric Le Roux has written a very lucid exposition of the Alpern genericity theorem. This theorem states that the same ergodic properties are generic in the set of volume-preserving measurable transformations and in the set of volume-preserving homeomorphisms. More precisely, endow with the weak topology, i.e., the coarsest generated by , for all measurable [...]
Orders of accumulation of entropy structures
Posted in Dynamics, talks, tagged Dynamics, entropy structure, ergodic theory, set theory, symbolic extension, topological dynamics on January 14, 2010 | Leave a Comment »
Kevin McGoff gave a talk at Orsay on his work on the theory of entropy srtuctures and symbolic extensions. This theory was founded by Mike Boyle and Tomasz Downarowicz, among others. This theory relates the continuity properties of the measure-theoretic entropy function with the existence of symbolic topological extensions with measure-theoretic entropies as close as [...]
Ergodicity of partially hyperbolic symplectomorphisms
Posted in Dynamics, Meetings, talks, tagged Dynamics, ergodic theory, generic dynamics, partial hyperbolicity, smooth dynamics, stable ergodicity on November 27, 2009 | Leave a Comment »
Amie WILKINSON presented new results towards the Pugh-Shub Stable ergodicity conjecture. In particular, with A. AVILA and J. BOCHI, she proved that ergodicity is generic in C^1 partially hyperbolic symplectomorphisms. She noted that, by a result of SAGHIN and Z. XIA, a stably ergodic symplectomorphism is automatically partially hyperbolic (which fails for conservative diffeomorphisms by [...]
Lower bounds for Hausdorff dimension
Posted in Dynamics, news, papers, tagged Dynamics, entropy, ergodic theory, Hausdorff dimension on October 13, 2009 | Leave a Comment »
A classical theorem (Marstrand 1954) asserts that, given any Borel subset , the obvious inequality of the Hausdorff dimensions: is in fact an equality for almost all orthogonal projections . As is often the case it is usually very dificult to prove equality for a given projection. Preliminary description: Michael HOCHMAN and Pablo SCHMERKIN have [...]
