Department of mathematics

Office: Eckhart 330

Eckhart Hall

5734 S University Ave

Chicago IL, 60637.

EMAIL: daviobata at uchicago dot edu

I am a Dickson Instructor at the University of Chicago. I study dynamical systems and ergodic theory. I am particularly interested in smooth ergodic theory, rigidity problems, statistical properties of dynamical systems and hyperbolic dynamics. I completed my Ph.D. in 2019 at the Université Paris-Sud, under the supervision of Sylvain Crovisier, and at the Federal University of Rio de Janeiro (UFRJ), under the supervision of Alexander Arbieto.

"Ser feliz sem motivo é a mais autêntica forma de felicidade."

*On the genericity of positive exponents of conservative skew products with two-dimensional fibers. (with Mauricio Poletti). To appear in Journal of Dynamics and Differential Equations, 2021.**New examples of stably ergodic diffeomorphisms in dimension 3. (with Gabriel Núñez and Jana Rodriguez Hertz) Nonlinearity, v.34, n.3, p.1352-1365, 2021.**Uniqueness of the measure of maximal entropy for the standard map. Commentarii Mathematici Helvetici, v.96, n.1, p. 79-111, 2021.**Symmetries of vector fields: The diffeomorphism centralizer. To appear in Discrete and Continuous Dynamical Systems, v.41, n.10, p. 4943-4957, 2021.**A new example of robustly transitive diffeomorphism. (with Pablo Carrasco). To appear in Mathematical Research Letters, 2020.**On the centralizer of vector fields: Criteria of triviality and genericity results. (with Martin Leguil and Bruno Santiago). Mathematische Zeitschrift, v.297, n1-2, p.283-337, 2021.**On the stable ergodicity of Berger-Carrasco's example. Ergodic Theory and Dynamical Systems, v.40, n.4, p. 1008-1056, 2020.**On the stable ergodicity of diffeomorphisms with dominated splitting. Nonlinearity, v.32, n.2, p.445, 2019.**On attractors and their basins. (with Alexander Arbieto) Involve, a Journal of Mathematics, v.8, n.2, p.195-209, 2015.**On bi-Lyapunov stable homoclinic classes. (with Alexander Arbieto, Bernardo Carvalho and Welington Cordeiro)*

Bulletin of the Brazilian Mathematical Society, New Series, v.44, n.1, p.105-127, 2013.

*Open sets of partially hyperbolic skew products having a unique SRB measure, preprint, 2021.**Rigidity of u-Gibbs measures near conservative Anosov diffeomorphisms on T3 (with Sebastien Alvarez, Martin Leguil and Bruno Santiago), preprint, 2022.*

*Appendix on the book "Entropy, Lyapunov exponents, and rigidity of group actions", by Aaron Brown, with appendices by Dominique Malicet, Bruno Santiago, Davi Obata, Sebastien Alvarez and Mario Roldán. Edited by Michele Triestino. Ensaios Matemáticos 33, 2019.*

O sonho é que leva a gente para a frente. Se a gente for seguir a razão, fica aquietado, acomodado."

*Ergodicité stable et mesures physiques pour des systèmes dynamiques faiblement hyperboliques. Ph.D. thesis at Université Paris-Sud under the supervision of Sylvain Crovisier. December 2019.**Symmetries of flows: The vector field and diffeomorphism centralizer. Ph.D. thesis at UFRJ under the supervision of Alexander Arbieto. July 2019.**On the star property. Master's thesis under the supervision of Alexander Arbieto. 2015.**Resultados na Teoria de Dinâmica Genérica. (in portuguese) Undergraduate monograph under the supervision of Alexander Arbieto. 2010.**On the Holonomies of strong stable foliations.**A simple proof of Birkhoff's Theorem.*

"Às vezes ouço passar o vento; e só de ouvir o vento passar, vale a pena ter nascido."

All the informations about the classes I am teaching will be available on Canvas.

It follows a list of a few websites that I like and the personal pages of a few mathematicians.