Frontiers of Operator Dynamics
September 28 – October 2, 2015
Dynamics of linear operators, often seen as dynamics of the corresponding discrete or continuous operator semigroup, is a mature but at the same time steadily evolving field serving as a common denominator for many other areas of mathematics, such as for instance ergodic theory, complex analysis, harmonic analysis and the theory of partial differential equations. It consists in the study of the long-time behaviour of orbits of certains classes of operators or semigroups acting on Banach or Fréchet spaces, both from the topological and from the ergodic point of view.

The aim of the meeting « Frontiers of Operator Dynamics » is to bring together researchers whose main interests interact with issues pertaining to the study of qualitative and quantitative properties of operator orbits (or operator semigroups) as well as experts in ergodic theory, and to initiate a fruitful interchange of ideas from complementary areas of expertise. In particular, it will be one of the main goals of the workshop to underline the interactions between:

– classical ergodic theory with emphasis on operator aspects, such as the study of convergence of averages, of recurrence, of joining of dynamical systems, and of rigidity phenomena;

– dynamics of operator semigroups, with the study of conditions implying convergence of orbits, as well as of the rates of convergence, and the investigation of their « good » asymptotic properties such as stability or hyperbolicity, as well as their « bad » asymptotic properties such as cyclicity and mixing;

– dynamics of linear operators, i.e. the study of dynamical systems given by the action of a bounded linear operator on a Banach space, and the investigation of topological properties (such as hypercyclicity) as well as of ergodic phenomena in this context.

Scientific Committee

Vitali Bergelson (Ohio State University)
Alexander Borichev (Aix-Marseille Université)
Ralph Chill (TU Dresden)
Eli Glasner (Tel Aviv University, Israel)
Sophie Grivaux (Université Lille 1)
Marius Lema
ńczyk (Nicolaus Copernicus University Torun)

Organizing Committee

Sophie Grivaux (Université Lille 1)
Marius Lemańczyk (Nicolaus Copernicus University Torun)
Yuri Tomilov (Polish Academy of Sciences)


Distributional limits of positive, ergodic stationary processes & infinite ergodic transformations (slides)

Convergence of orbits and compactness

Convergence of nonconventional ergodic averages (slides)

Sets of integers determined by operator-theoretical results

Rates of decay associated with operator semigroups (slides)

Common hypercyclic vectors for high dimensional families of operators

Potpourri of Open Problems and Conjectures in Linear Dynamics and Ergodic Theory.

Random and pseudo-random Taylor series

Markov operators, reverse martingles and ergodic theorems for group actions

Quantified versions of Ingham’s Tauberian theorem

Almost mixing of all orders Z2-actions, Ledrappier’s example and the CLT

Eigenvalues of minimal Cantor systems (slides)

Weighted ergodic theorems (slides)

On the Banach spectral problem in ergodic theory and the polynomial
flatness problem with connection to the Mahler problem and related topics

Hypercyclic scalar sets

A Bohl–Bohr–Kadets type theorem characterizing Banach spaces not containing c_0

Birkhoff and Oseledets genericity along curves (slides)

  • Alexander Gomilko (Nicholas Copernicus University, Torun)

Rates in mean ergodic theorems: inverse results

Upper frequently hypercyclic operators

On some operator-theoretic aspects of ergodic theory (slides)

On asymptotics of Arnold tongues for some families of flows on 2-tori

Strange products of orthogonal projections (slides)

Symmetrization of Markov operators

Some remarks regarding ergodic operators (slides)

Linear chaos and frequent hypercyclicity (slides)

Mean ergodic theorem for polynomial subsequences (slides)

  • Marina Murillo Arcila (University ‘Politecnica Valencia’)

Frequently hypercyclic translation semigroups

Two semigroups connected with the infinite symmetric group, their representations and random walk on graded graphs

On the shadowing property in linear dynamics

Automorphism groups of subshifts with low complexity (slides)

r-Bohr sequences which are not (r+1)-Bohr

Asymptotics of infinite systems of ODEs (slides)

On one-parameter Koopman groups (slides)

Commutator criteria for strong mixing (slides)