MINI WORKSHOP ON DYNAMICAL SYSTEM - Monday and Tuesday next week

[ICTP Math Section]

_*MINI WORKSHOP ON DYNAMICAL SYSTEM*_


Everyone is welcome to attend
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*Monday 7 August and Tuesday 8 August*

*Venue: ICTP, Luigi Stasi Seminar Room* (Leonardo Building, first floor)


PROGRAMME:

*Monday 11:15-12:15 *
Speaker: *Amin Talebi (Sharif University, Iran)*
Title: _Statistical instability and non-statistical dynamics_
Abstract:  Previously, the notion of statistical stability had been 
defined for certain classes of maps, having some specified properties, 
such as existence of unique phisical measure with full basin. We will 
give a general formalization of this notion in the general case, 
regardless of the statistical properties of the maps we consider. Then 
we will show how statistical instability can imply the existence of 
non-statistical maps, which are those maps for which a set of positive 
measure have non-convergent sequence of empirical measures.


*Monday 13:30-14:30 *
Speaker: *Hamza Ounesli (ICTP & SISSA, Italy)*
Title: _Dynamics of uniformly expanding maps in low regularity_
Abstract: in this seminar I will start by recalling the history behind 
the ergodic theory of expanding maps and the techniques involved in 
their study, as we will see, these techniques were developed under the 
assumption that our maps are regular enough. The main topic of the 
seminar is to explore the underground world of very low regular 
expanding maps.


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*Tuesday 11:00-12:00 *
Speaker: *Asad Ullah (Universidade de Beira Interior, Portugal)*
Title: _Decay of Correlations via Induced Weak Gibbs Markov maps_
Abstract: L. S. Young introduced induced Gibbs Markov maps in 1998 and 1999.
She showed that the existence of induced Gibbs Markov maps with 
integrable return time implies the existence of an exact invariant 
absolutely continuous probability measure with respect to reference 
measure,  and the rate of decay of correlations is related to the tail 
of the return time.  In this talk, I will discuss how to obtain similar 
results under weaker assumptions, which allows the induced map not 
necessarily to be a full branch.
/This is a joint work with Helder Vilarinho, UBI & CMA-UBI/


*Tuesday 13:00-14:00 *
Speaker: *Bernardo Carvalho (Rome Tor Vergata, Italy)*
Title: _Chaos theory and hyperbolic dynamics_
Abstract: In this talk I will discuss relations between chaotic and 
hyperbolic systems. More specificaly, how we can obtain known results 
from hyperbolic dynamics using stronger notions of sensitivity to 
initial conditions. I will briefly explain expansiveness, topological 
hyperbolicity, cw-expansiveness, cw-hyperbolicity, and first-time 
sensitivity.


*Tuesday 14:15-15:15*
Speaker: *Giovanni Panti (University of Udine, Italy)*
Title: _Iterated function systems, cookie-cutters, and continued fractions_
Abstract: An iterated function system, possibly a graph-directed one, 
determines an attractor, which can also be seen as the repeller of a 
cookie-cutter map. In certain cases these maps are Gauss-like and amount 
to continued fraction algorithms. We present the basics of this 
crossroad between dynamics and number theory, focusing on open problems.