Dynamics Afternoon - Friday, 14 March 2025 (15:30 - 18:00) - VENUE: Luigi Stasi seminar room (ICTP Leonardo Da Vinci Building)

[ICTP Math Section]

Dynamics Afternoon

Friday, 14 March 2025 (15:30 - 18:00)

Venue: Luigi Stasi seminar room (Leonardo Da Vinci Building)
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15:30 Alexandre Delplanque (LPSM,Paris, France)

Title: Hyperbolic absolutely continuous measures for one-dimensional maps

Abstract: Given a dynamical system, we are interested in the asymptotic 
distribution of its orbits. We will focus on one-dimensional dynamics, 
and in particular we will present the following result:
If f is a C^r one-dimensional map, with r > 1, then Lebesgue-almost 
every point with a Lyapunov exponent larger than (log || f' 
||_infinity)/r is in the basin of an ergodic measure which is hyperbolic 
and absolutely continuous with respect to the Lebesgue measure.


16:00 Rizwan Ullah (SISSA, Trieste, Italy)

Title: Doubly Intermittent Singular Skew Products

Abstract: The statistical characteristics of interval maps having 
indifferent fixed points have been extensively investigated. A method to 
examine a comparable issue in higher dimensions is through the skew 
product system, which is a coupling of two systems non-autonomously.
This presentation will discuss a joint work with Stefano Luzzatto, where 
we analyzed a skew product system by coupling a uniformly expanding 
circle map with a double intermittent interval map exhibiting unbounded 
derivatives. By utilizing the inducing technique, we have demonstrated 
that this system possesses a unique ergodic absolutely continuous 
invariant probability (acip) with a polynomial decay of correlations.

/16:30 Break/


17:00 Rubio Gunawan (SISSA, Trieste, Italy)

Title: Uniformly Expanding Full Branch Maps with Attracting Fixed Point

Abstract: We prove the existence of a uniformly expanding full branch 
map that has an attracting fixed point. The map is given by infinitely 
many smooth branches, and the domains of the branches accumulate at 
zero. Zero is an attracting fixed point, and its basin of attraction has 
full measure. A key assumption is convexity on each branch. We apply the 
assumption to estimate measures of sets that are contained in the basin.

17:30 Jose Ferreira Alves (University of Porto, Porto, Portugal)

Title: Statistical stability in non-uniformly expanding dynamics

Abstract: In this talk we present some some recent results on the 
statistical stability of certain families of one-dimensional 
non-uniformly expanding maps. Joint work with Dalmi Gama and Stefano 
Luzzatto.

/https://indico.ictp.it/event/10986//

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Koutou Mabilo
ICTP Mathematics Group
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