Tuesday 4th October at 17:00 (ICTP)
“A geometric model for the natural extension of continued fraction maps”
Abstract: Just as classical “Floor” continued fractions induce the Gauss map on the real unit interval, other euclidean division algorithms (Ceiling, Even, Odd, NearestInteger, …) induce piecewise-fractional maps with integer coefficients. All these maps have natural extensions that can easily be described on an ad hoc basis.
We present a general framework for dealing with all these maps in a uniform way.
This is a call for the participation of all DinAmicI to the Prima Giornata DinAmica, our first social meeting to be held on 25 November at the Gran Sasso Science Institute in L’Aquila.
There will be seminars by Mauro Artigiani, Anna Miriam Benini and Marcello Seri in the morning. Whereas the afternoon will be devoted to the assembly of the DinAmicI, in which we will discuss possible directions of development of the group.
It is a pleasure to announce that our biennial meeting to be held in 2017, will take place in Rome in the week 5-9 June.
It will be sponsored by INdAM with the title
“Workshop INdAM - DinAmicI V - Modern Trends in the Ergodic Theory of Dynamical Systems”
and have agreed to be part of the scientific committee: Carlangelo Liverani, Yakov Sinai and Lai-Sang Young.
More information and a website will appear soon.
The workshop will be held at ICTP, Trieste, 19-23 June 2017. Particular emphasis will be devoted to the core topics which have benefited from the seminal contributions of Yakov Pesin: nonuniform hyperbolicity, dimension theory, thermodynamical formalism.
Speakers: Bunimovich, Buzzi, Denker, Dolgopyat, Hochman, A. Katok, S. Katok, Khanin, Ledrappier, Liverani, Luzzatto, Pesin, Pollicott, F. Rodriguez-Hertz, Sarig, Schmeling, Senti, Shub, Viana, Wilkinson, Zhang
Organizers: Dmitry Dolgopyat, Federico Rodriguez-Hertz, Omri Sarig. Local Organiser: Stefano Luzzatto.
Thursday 18th August at 14:30 (ICTP)
“Ergodicity of Surface Actions via Flag Manifold”
Abstract: This talk is devoted to study the ergodicity of smooth surface actions. We provide a sufficient condition for surface actions to be ergodic with respect to the Lebesgue measure. First, we address the main results obtained so far for the unit circle, as a main tool in higher dimensional. After that, by introducing the notion of flag manifold, we explain how rich minimality of sufficiently smooth action on the flag manifold may lead to the ergodicity of the initial action.
ICTP and the Istituto Nazionale di Alta Matematica (INdAM) have launched a joint program of “Research in Pairs” aimed to fund research project in Mathematics to be carried out in collaboration between mathematicians from developing countries and INdAM members either at ICTP in Trieste or in any research unit of INdAM (see the list at https://www.altamatematica.it/it/node/43).
Applications must be submitted using the online system https://e-applications.ictp.it/applicant/login/math_pairs; the deadline is 15 September 2016.
Thursday 4th August at 14:30 (ICTP)
“Geometric constructions of Equilibrium States”
Abstract: In this talk I’ll show a completely different construction of equilibrium states associated to Hölder potentials for hyperbolic systems, and indicate the necessary modifications to deal with certain partially hyperbolic cases. The key point for this extension is avoiding altoghether the use of symbolic dynamics and the Perron-Frobenious method. Time permiting I’ll discuss applications. This is a joint project with F.
Wednesday 17th August at 14:30 (ICTP)
“Martingale approximation for parametrised dynamical systems”
Abstract: In joint work with Alexey Korepanov and Zemer Kosloff, we prove statistical limit laws for sequences of the type \(\sum_{j=0}^{n-1}v_n\circ T_n^j\) where \(T_n\) is a family of nonuniformly hyperbolic transformations. The key ingredient is a new martingale-coboundary decomposition for nonuniformly hyperbolic transformations which is useful in the case when the family \(T_n\) is replaced by a fixed transformation \(T\), but which is particularly useful in the case when \(T_n\) varies with \(n\).
Mini-course on Double Resonances on December 12-16, 2016 Jean-Pierre Marco and Vadim Kaloshin will give a mini-course on
Double resonances in the problem of Arnold diffusion
during the week of December 12-16, 2016, in Institut Henri Poincaré (lecture room 201) in Paris. They will address such issues as normal forms along double resonances, singular cylinders, genericity, invariant sets, and local transitivity. The goal is to explain some of the technical details to the audience and to confront their viewpoints.
At the end of the Pisa-Hokkaido, 2016 summer school, there will be a small workshop involving dynamics.
Chaotic phenomena in mathematical models
(for general information on the whole school )
