Miniconference on Dynamical Systems 
and Ergodic Theory

Organizers:

Michael Benedicks and Håkan Eliasson

Because of the thesis defenses of Kristian Bjerklöv and Maria Saprykina on October 3 and October 6 we have several distinguished guests at our department and we have taken the opportunity to arrange a miniconference on Saturday October 4.

The lectures will take place in Seminar Room 3733 Lindstedtsvägen 25, KTH.

PROGRAMME

10.00 - 10.50 Jean Paul Thouvenot, Paris A specific information theory for positive entropytransformations
11.10 - 12:00 Mariusz Lemanczyk, Torun On the disjointness problem in ergodic theory
ABSTRACT: We will be interested in a notion of extremal non-similarity of dynamical systems. This is the concept of disjointness due to H. Furstenberg. Related notions: joinings and Markov operators will be presented. We will use this to show that some smooth flows on surfaces are disjoint from some flows of probability origin.

12.00 - 13.30 LUNCH
13.30 - 14.20 Russel Johnson, Firenze On Cantor spectrum for the quasi-periodic Schrödinger operator
ABSTRACT:  In recent years there has been remarkable progress in understanding the spectral properties of the quasi-periodic Schrödinger operator. Important contributions have been made by Bjerklöv, Broer, Eliasson, Krikorian, Puig, and Simò. Much of their work has been carried out under the assumptions that the potential is smooth and that the frequencies satisfy a diophantine condition. It turns out that certain results hold true under the "orthogonal" hypotheses: non-smooth potentials and well-approximable frequency vectors. The main tools used in proving these results are the exponential dichotomy concept and the rotation number. The work to be discussed was carried out jointly with R. Fabbri and R. Pavani.
14.40 - 15.30 Raphael Krikorian, Paris Quasi-periodic Schrödinger cocycles almost always have positive Lyapunov exponents or are Floquet reducible (Joint work with A. Avila)
ABSTRACT: The statement of the title (for discrete Schrödinger cocycles over diophantine translation of the circle and smooth or analytic potential) has also interesting consequences concerning the spectrum of the one-dimensional quasi-periodic Schrödinger equation: for example, the (Lebesgue) measure of the singular spectrum is zero for a.e frequency in the base. Also, we can prove the Aubry-Andre conjecture on the (Lebesgue) measure of the spectrum of the almost-Mathieu operator

 

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2003-09-19