Yuri Lima · Matemática

Pesquisa

Áreas de investigação, publicações, livros, financiamentos e o projeto Jangada Dinâmica.

Áreas

Dynamical Systems

Dinâmica hiperbólica, não uniformemente hiperbólica e parcialmente hiperbólica; dinâmica simbólica para difeomorfismos de superfície e fluxos em dimensão arbitrária.

Ergodic Theory

Medidas de máxima entropia, estados de equilíbrio, decaimento de correlações e teoremas limite para sistemas caóticos, incluindo bilhares e fluxos geodésicos.

Probability

Teoremas limite para sistemas dinâmicos, urnas de Pólya em grafos e hipergrafos, processos estocásticos com reforço.

Combinatorics

Combinatória aditiva, projeções de conjuntos de Cantor e teoremas tipo Marstrand.

Jangada Dinâmica

A Jangada Dinâmica é um projeto de pesquisa, formação e integração científica criado para fortalecer a comunidade de Sistemas Dinâmicos e Teoria Ergódica no Brasil. A iniciativa busca conectar pesquisadores, formar novos estudantes, ampliar a diversidade acadêmica e consolidar um ambiente de pesquisa internacionalmente competitivo.

  • · Formação de novos pesquisadores
  • · Organização de eventos científicos
  • · Cooperação internacional
  • · Produção de material educacional
  • · Fortalecimento da pesquisa matemática brasileira
Instituto Serrapilheira ↗

Financiamentos & Projetos Ativos

  • FUNCAP UniversalR$ 37,000Nov 2023 – Nov 2025
  • Instituto SerrapilheiraR$ 1,400,000Nov 2019 – Jul 2027
    Jangada Dinâmica: boosting dynamical systems in Brazil's Northeastern region
  • Royal Society — Newton Advanced Fellowship£ 39,900Apr 2018 – Mar 2020
    Decay of correlations and statistical properties of high-dimensional dynamical systems
  • Instituto SerrapilheiraR$ 100,000Mar 2018 – Aug 2019
    Symbolic dynamics and non-uniform hyperbolicity
  • AMS Simons Travel GrantAug 2014 – Aug 2015
  • CAPES / Weizmann 2012Jun 2012 – Jun 2014
    Infinite ergodic theory

Livros

  • Olimpíadas Cearenses de Matemática de 2014 a 2024

    SBM · — · 218 páginas
    ISBN: 9788583372530

  • Introdução aos Sistemas Dinâmicos

    SBM · 2025 · 178 páginas
    ISBN: 9788583372554

  • Alice no País da Dinâmica: Sistemas Dinâmicos Para o Ensino Médio

    LF Editorial · 2025 · 116 páginas
    ISBN: 978-6555634150

  • Treinamento Olímpico

    with C. Augusto, S. Feitosa, B. Holanda and C. Thiago
    SBM · 2020 · 410 páginas
    ISBN: 978-65-990395-2-2

  • Treinamento Cone Sul, Volume 2

    with S. Feitosa, B. Holanda and C. Thiago
    Realce Editora · 2010 · 174 páginas
    ISBN: 978-85-89105-37-8

  • Treinamento Cone Sul, Volume 1

    with C. Augusto, S. Feitosa and B. Holanda
    Realce Editora · 2007 · 114 páginas
    ISBN: 858921555-5

Publicações

29 de 29

2026

#29Preprint2026

Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces

with C. Matheus and I. Melbourne
· 34 pages
arXiv:2512.11051
#28Preprint2026

Uniqueness of the measure of maximal entropy for geodesic flows on surfaces

with D. Obata and M. Poletti
· 14 pages
arXiv:2511.22022
#25Published2026

Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia

with C. Matheus and I. Melbourne
Comm. Math. Phys. · 407, 130 (2026)
DOI
#24Online First2026

Measures of maximal entropy for non-uniformly hyperbolic maps

with D. Obata and M. Poletti
J. Eur. Math. Soc. · Published online first, 39 pages
DOI

2025

#27Preprint2025

Symbolic dynamics for non-uniformly hyperbolic flows in high dimension

with J. C. Mongez and J. P. Nascimento
· 82 pages
arXiv:2509.09050
#26Accepted2025

Equilibrium states by synchronization, symbolic extensions, and factors

with K. Gelfert and D. Kwietniak
Nonlinearity · Accepted
arXiv:2503.18193
#23Published2025

Symbolic dynamics for large non-uniformly hyperbolic sets of three dimensional flows

with J. Buzzi and S. Crovisier
Adv. Math. · 479 (2025), Paper No. 110410
DOI
#22Published2025

Pólya urns on hypergraphs

with P. Alves and M. Barros
Nonlinearity · 38 (2025), no. 7, 075004, 20 pp.
DOI
#21Published2025

Homoclinic classes of geodesic flows on rank 1 manifolds

with M. Poletti
Proc. Amer. Math. Soc. · 153 (2025), no. 4, 1611–1620
DOI

2024

#20Published2024

Symbolic dynamics for nonuniformly hyperbolic maps with singularities in high dimension

with E. Araujo and M. Poletti
Mem. Amer. Math. Soc. · 301 (2024), no. 1511
DOI
#19Published2024

Polynomial decay of correlations for nonpositively curved surfaces

with C. Matheus and I. Melbourne
Trans. Amer. Math. Soc. · 377 (2024), no. 9, 6043–6095
DOI
#18Published2024

Lyapunov exponents and nonadapted measures for dispersing billiards

with V. Climenhaga, M. Demers, and H.-K. Zhang
Comm. Math. Phys. · 405, 24 (2024)
DOI

2023

#17Published2023

Examples of d-sets with irregular projection of Hausdorff measures

with C. G. Moreira
Bull. Braz. Math. Soc. (N.S.) · 54 (2023), no. 2, Paper No. 28, 4 pp.
DOI

2021

#16Published2021

Symbolic dynamics for nonuniformly hyperbolic systems

Ergodic Theory Dynam. Systems · 41 (2021), no. 9, 2591–2658
DOI

2020

#15Published2020

Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems

with L. Backes, M. Poletti, and P. Varandas
Ergodic Theory Dynam. Systems · 40 (2020), no. 11, 2947–2969
DOI
#14Published2020

Symbolic dynamics for one dimensional maps with nonuniform expansion

Ann. Inst. H. Poincaré Anal. Non Linéaire · 37 (2020), no. 3, 727–755
DOI

2019

#13Published2019

Symbolic dynamics for three dimensional flows with positive topological entropy

with O. Sarig
J. Eur. Math. Soc. · 21 (2019), no. 1, 199–256

2018

#12Published2018

Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities

with C. Matheus
Ann. Sci. Éc. Norm. Supér. · 51 (2018), no. 1, 1–38

2016

#11Published2016

Ergodic properties of skew products in infinite measure

with P. Cirilo and E. Pujals
Israel J. Math. · 214 (2016), no. 1, 43–66
#10Published2016

Graph-based Pólya's urn: completion of the linear case

Stoch. Dyn. · 16 (2016), no. 2, 13pp.
#9Published2016

Ergodic properties of equilibrium measures for smooth three dimensional flows

with F. Ledrappier and O. Sarig
Comment. Math. Helv. · 91 (2016), no. 1, 65–106

2015

#8Published2015

A generalized Pólya's urn with graph based interactions

with M. Benaïm, I. Benjamini, and J. Chen
Random Structures Algorithms · 46 (2015), no. 4, 614–634

2014

#7Published2014

Annihilation and coalescence on binary trees

with I. Benjamini
Stoch. Dyn. · 14 (2014), no. 3, 11pp.
#6Published2014

An Abramov formula for stationary spaces of discrete groups

with Y. Hartman and O. Tamuz
Ergodic Theory Dynam. Systems · 34 (2014), no. 3, 837–853
#5Published2014

Law of large numbers for certain cylinder flows

with P. Cirilo and E. Pujals
Ergodic Theory Dynam. Systems · 34 (2014), no. 3, 801–825
#4Published2014

A Marstrand theorem for subsets of integers

with C. G. Moreira
Combin. Probab. Comput. · 23 (2014), no. 1, 116–134

2012

#3Published2012

Z^d-actions with prescribed topological and ergodic properties

Ergodic Theory Dynam. Systems · 32 (2012), no. 1, 191–209

2011

#2Published2011

Yet another proof of Marstrand's theorem

with C. G. Moreira
Bull. Braz. Math. Soc. · 42 (2011), no. 2, 331–345
#1Published2011

A combinatorial proof of Marstrand's theorem for products of regular Cantor sets

with C. G. Moreira
Expo. Math. · 29 (2011), no. 2, 231–239