Starts 7 Aug 2023 11:15
Ends 8 Aug 2023 15:00
Central European Time
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Mini-Workshop on Dynamical Systems
ICTP
Leonardo Building - Luigi Stasi Seminar Room
The ICTP Mathematics Section is organizing a Mini-Workshop on Dynamical System to be held in the Luigi Stasi Seminar Room (Leonardo Building, first floor) on Monday 7 August and Tuesday 8 August.
Below is the programme of the event.
Monday 7 August
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.
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.
Tuesday 8 August
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
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.
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.
Below is the programme of the event.
Monday 7 August
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.
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.
Tuesday 8 August
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
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.
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.