Dynamics Archives for Academic Year 2017


Infinite mixing for one-dimensional maps with an indifferent fixed point

When: Thu, August 31, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Marco Lenci (Universita' di Bologna) - http://www.dm.unibo.it/~lenci/
Abstract: In the first part of the talk, I will give some background on the
question of mixing for dynamical systems preserving an infinite
measure (a.k.a. 'infinite mixing'). Then I will recall and discuss the
definitions of 'infinite-volume mixing' that I have introduced in
recent years, with a survey on some examples of dynamical systems
which verify or do not verify such definitions. Among these examples
there will be one-dimensional intermittent maps, the subject of recent
work with C. Bonanno and P. Giulietti.
In the second part of the talk, I will better state the results for
the intermittent maps: they comprise a class of expanding maps of
[0,1] with a 'strongly neutral' fixed point in 0 and a class of
expanding maps of the real line with strongly neutral fixed point at
infinity. I will give a sketch of how some of the definitions of
infinite-volume mixing are proved or disproved. Finally I will show
how one property, called global-local mixing, entails certain limit
theorems for our intermittent maps.

Ground states for Frenkel-Kontorova models on quasicrystals

When: Thu, September 7, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Rodrigo Trevino (UMD) - http://trevino.cat
Abstract: The Frenkel-Kontorova model was first proposed in the 1930's to describe the structure and dynamics of a crystal lattice in the vicinity of a dislocation core, and by now has found many uses outside of solid state physics. Viewed from a dynamical systems point of view, it exhibits a lot of rich behavior tied to all sorts of great theories (e.g. KAM theory and Aubry-Mather theory) and fundamental open questions (e.g. Lyapunov exponents for the standard map).

I will talk about this model in the setting where the crystal is aperiodic. In this setting, most of the dynamics are no longer available, but some tools developed to study the (periodic) classical model are still useful. I will talk about how one of them in particular, the so-called anti-integrable limit, is useful to find ground states (also known as equilibrium configurations). No background on the model will be assumed.

Mixing and local limit theorem for some hyperbolic flows

When: Thu, September 28, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Peter Nandori (UMD) - http://math.umd.edu/~pnandori/
Abstract: We consider a special flow over a mixing map with some hyperbolicity.
In case the roof function is square integrable, we find a set of conditions, under which the flow is mixing and also satisfies the local limit theorem. In case the roof function is non-integrable, we identify another set of conditions that imply Krickeberg mixing. The most important condition is the local limit theorem for the underlying map. We check that the conditions are satisfied for some examples, such as Axiom A flows, Sinai billiards, geometric Lorenz attractors (finite measure case) and suspensions over Pomeau-Manneville maps (finite and infinite measure cases). The talk is based on joint work with Dmitry Dolgopyat.

TBA

When: Thu, October 19, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Vadim Kaloshin (UMD) - https://www.math.umd.edu/~vkaloshi/
Abstract: TBA

TBA

When: Thu, October 26, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Alex Blumenthal (UMD) - http://math.umd.edu/~alexb123/
Abstract: TBA

TBA - UNUSAL DATE

When: Tue, November 7, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Jianlu Zhang (UMD) -
Abstract: TBA

TBA

When: Thu, November 16, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Fumihiko Nakamura (Hokkaido University ) -
Abstract: TBA

TBA

When: Thu, December 7, 2017 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Thibaut Castan (UMD) -
Abstract: TBA