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 [...]
Posts Tagged ‘Dynamics’
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 »
Cellular Automata Modeling Reliable Computers: 3D
Posted in Dynamics, Meetings, talks, tagged computation, Dynamics, multidimensional shifts, probability theory, symbolic dynamics on March 26, 2010 | Leave a Comment »
Real-world computers make mistakes, in the sense that once in a while an instruction is executed incorrectly, perhaps because of a corrupted disk. One could naively think that, given, a maximum acceptable probability of an incorrect final result, this would impose a bound on the complexity of possible computation or require an exponential number of [...]
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 [...]
Dilation factors of pseudo-Anosov homeomorphisms
Posted in Dynamics, talks, tagged Dynamics, flat surfaces, moduli space, pseudo-Anosov, smooth dynamics, surface dynamics, topology on January 14, 2010 | Leave a Comment »
Erwan Lanneau gave a talk in Orsay about his work on surfaces of translation. Pseudo-Anosov homeomorphisms are homeomorphisms of such surfaces which are affine away from the singular set of the surface and whose differential is hyperbolic. The dilation factor is the dominant eigenvalue of that differential. It is a Perron number. The minimum of [...]
C^2 surface diffeomorphisms always have a symbolic extension
Posted in Dynamics, news, papers, tagged Dynamics, entropy, entropy structure, smooth dynamics, smooth ergodic theory, symbolic extension, topological dynamics on December 10, 2009 | Leave a Comment »
Most of topological dynamics studies systems of the form where is a continuous self-map and is a compact metric space. One approach is to “reduce” such systems to symbolic dynamical system, i.e., where is a closed subset of and such that . J. Auslander asked about the obstructions for a topological system to have a [...]
Discontinuity of the topological entropy for Lozi maps
Posted in Dynamics, news, papers, tagged continuity of the entropy, Dynamics, entropy, examples, hyperbolicity, Lozi maps, piecewise affine dynamics, surface dynamics on December 10, 2009 | Leave a Comment »
I have shown that, like diffeomorphisms, piecewise affine surface homeomorphisms are approximated in entropy by horseshoes, away from their singularities. It follows in particular that their topological entropy is lower-semicontinuous: a small perturbation cannot cause a macroscopic drop in entropy. The continuity of the entropy for such maps had been an open problem for some [...]
A measure of maximal entropy (by A. Chéritat)
Posted in Dynamics, tagged Dynamics, maximal entropy measure, pictures, smooth ergodic theory on December 3, 2009 | Leave a Comment »
A measure of maximal entropy of the rational fraction on the Riemann sphere according to Arnaud Chéritat. It describes the distribution of preimages of almost all points.
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 [...]
Sylvain CROVISIER’s HDR
Posted in Dynamics, news, talks, tagged bifurcations, closing lemma, Dynamics, generic dynamics, partial hyperbolicity, smooth ergodic theory, topological dynamics on November 27, 2009 | Leave a Comment »
On November 25th, 2009, Sylvain CROVISIER defended his habilitation à diriger des recherches titled Perturbation de la dynamique de difféomorphismes en petite régularité. He first explained basic perturbation techniques: the Anosov-Katok procedure: you use more and more distorted conjugacies such that the limiting dynamics has new properties; the closing lemma of Pugh and the subsequent [...]
