1. Santiago Martinchich (IMERL-Uruguay) 14:00-14:40

Title: Partially hyperbolic diffeomorphisms acting quasi-isometric on the center

Abstract: A key tool in the study of partially hyperbolic diffeomorphisms is the presence of invariant foliations. Given an invariant foliation tangent to the center bundle, we say that the diffeomorphism acts quasi-isometrically on it if there exist two constants r>0 and R>0 such that any pair of points at center distance less than r stay at distance less than R for every positive and negative iterate. I will present the following classification result for 3-dimensional transitive partially hyperbolic diffeomorphisms acting quasi-isometrically on the center: modulo finite lift and iterates, the system is a skew-product (the center foliation is uniformly compact) or is a discretized Anosov flows. Joint work with Marcielis Espitia and Rafael Potrie.

2. Ygor Arthur (Unicamp) 14:50-15:30

Título: Construction of Partially Hyperbolic Geodesic Flows via conformal deformation
Abstract: In this talk we are going to present a construction of examples of partially hyperbolic geodesic flows that are not of Anosov type. This problem was first approached by Carneiro and Pujals. Their construction is based on deforming the Riemannian metric along a closed geodesic in order to break the hyperbolic behavior. Based on their work, we propose a new construction with several advantages to analyze the remaining hyperbolic behavior. With the new construction, we can have finer curvature estimates and prove ergodicity and uniqueness of measure of maximal entropy in some cases.

3. Pedro Griguol de Mattos (Unicamp) 16:00-16:40
Título: Metric Entropy and Folding Entropy of a Bilateral Shift with Two Alphabets
Abstract: In this talk, we introduce a construction for a bilateral shift space using two distinct finite alphabets: one encoding the future behavior of a point and the other representing its past. This symbolic space provides a framework for encoding endomorphisms, or non-invertible dynamical systems. We calculate both the Kolmogorov-Sinai (metric) entropy and the folding entropy of the shift, demonstrating their relationship in this context. The folding entropy, originally introduced by Ruelle, serves as a measure of non-invertibility of the system.

4. Jérôme Buzzi (Paris-Saclay) 16:50-17:30
Title: Exponential mixing MME for some diffeomorphisms with dominated splitting

Abstract: For many diffeomorphisms with partial hyperbolicity or dominated splitting, the measure maximizing the entropy (or MMEs) has been shown to be unique or with finite multiplicity. Many such examples can be revisited using the notion of strong positive recurrence recently developed by S. Crovisier, O. Sarig, and myself - especially in its characterization as a property of Lyapunov exponents. In the best cases, we obtain exponential mixing from already known estimates. We will see that many questions remain nonetheless open.