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Documents  Tomilov, Yuri | enregistrements trouvés : 8

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Research talks;Analysis and its Applications;Dynamical Systems and Ordinary Differential Equations

For any countable group, and also for any locally compact second countable, compactly generated topological group, $G$, there exists a "universal" hypercyclic representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of $G$. I will discuss the original proof of this theorem (a joint work with Benjy Weiss) and then, at the end of the talk, say some words about the development of this idea and its applications as expounded in a subsequent work of Sophie Grivaux. For any countable group, and also for any locally compact second countable, compactly generated topological group, $G$, there exists a "universal" hypercyclic representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of $G$. I will discuss the original proof of this theorem (a joint work with Benjy Weiss) and then, at the end of the talk, say some words about ...

37A15 ; 37A05 ; 37A25 ; 37A30 ; 47A16 ; 47A67 ; 47D03

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- 346 p.
ISBN 978-83-86806-36-2

Banach center publications , 0112

Localisation : Périodique 1er étage

théorie des opérateurs # analyse fonctionnelle # analyse numérique

47-06 ; 46-06 ; 65-06 ; 00B25

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- ix; 496 p.
ISBN 978-3-319-18493-7

Operator theory: advances and applications , 0250

Localisation : Collection 1er étage

semigroupe d'opérateurs # équation aux dérivées partielles # martingale # transformée de Hilbert # algèbre de Banach # algèbre de Neumann # opérateur de Schrödinger # régularité maximale # multiplicateur de Fourier # interpolation # théorème taubérien # induction transfinie # magie de Cantor

47-06 ; 42-06 ; 47D03 ; 30-XX ; 35-XX ; 42-XX ; 46-XX ; 47-XX

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- 328 p.
ISBN

Banach center publications , 0075

Localisation : Salle des périodiques 1er étage

théorie des opérateurs

47-06

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Research talks;Dynamical Systems and Ordinary Differential Equations

Let us say that a continuous linear operator $T$ acting on some Polish topological vector space is ergodic if it admits an ergodic probability measure with full support. This talk will be centred in the following question: how can we see that an operator is or is not ergodic? More precisely, I will try (if I’m able to manage my time) to talk about two “positive" results and one “negative" result. The first positive result says that if the operator $T$ acts on a reflexive Banach space and satisfies a strong form of frequent hypercyclicity, then $T$ is ergodic. The second positive result is the well-known criterion for ergodicity relying on the perfect spanning property for unimodular eigenvectors, of which I will outline a “soft" Baire category proof. The negative result will be stated in terms of a parameter measuring the maximal frequency with which (generically) the orbit of a hypercyclic vector for $T$ can visit a ball centred at 0. The talk is based on joint work with Sophie Grivaux. Let us say that a continuous linear operator $T$ acting on some Polish topological vector space is ergodic if it admits an ergodic probability measure with full support. This talk will be centred in the following question: how can we see that an operator is or is not ergodic? More precisely, I will try (if I’m able to manage my time) to talk about two “positive" results and one “negative" result. The first positive result says that if the ...

47A16 ; 47A35 ; 37A05

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Research talks;Dynamical Systems and Ordinary Differential Equations

I will describe the main features and methods of a strictly operator-theoretic/functional-analytic perspective on structural ergodic theory in the spirit and in continuation of a recent book project (with T.Eisner, B.Farkas and R.Nagel). The approach is illustrated by a review of some classical results by Abramov on systems with quasi-discrete spectrum and by Veech on compact group extensions (joint work with N.Moriakov).

37A30 ; 37A35 ; 37A55 ; 37B05 ; 47A35 ; 47Nxx ; 22CXX

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Research talks;Dynamical Systems and Ordinary Differential Equations

We will formulate and discuss various problems and results at the junction of Ergodic Theory and Linear Dynamics.

37-XX

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Research talks;Dynamical Systems and Ordinary Differential Equations

General theory of operator semigroups provides abstract results which can be used to obtain optimal rates of decay or convergence in many evolution equations or dynamical systems. I will describe the abstract results, and indicate how they are obtained and how they can be applied in examples.

47D06 ; 34D05 ; 34G10 ; 47B38

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