Dynamics Afternoon
 
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.