Luis Barreira



Books

  1. (with Ya. Pesin) Lyapunov Exponents and Smooth Ergodic Theory, University Lecture Series 23, American Mathematical Society, 2002.
  2. (with Ya. Pesin) Nonuniform Hyperbolicity, Encyclopedia of Mathematics and Its Applications 115, Cambridge University Press, 2007.
  3. (with C. Valls) Stability of Nonautonomous Differential Equations, Lecture Notes in Mathematics 1926, Springer, 2008.
  4. Dimension and Recurrence in Hyperbolic Dynamics, Progress in Mathematics 272, Birkhäuser, 2008. Ferran Sunyer i Balaguer Prize 2008
  5. Análise Complexa e Equações Diferenciais, Colecção Ensino da Ciência e da Tecnologia 30, IST Press, 2009.
  6. (with C. Valls) Equações Diferenciais: Teoria Qualitativa, Colecção Ensino da Ciência e da Tecnologia 33, IST Press, 2010.
  7. (with C. Valls) Exercícios de Análise Complexa e Equações Diferenciais, Colecção Apoio ao Ensino f, IST Press, 2010.
  8. (with C. Valls) Exercícios de Álgebra Linear, Colecção Apoio ao Ensino g, IST Press, 2011.
  9. Analyse Complexe et Équations Différentielles, Enseignement Sup - Mathématiques, EDP Sciences, 2011.
  10. (with C. Valls) Analyse Complexe et Équations Différentielles - Exercices Corrigés, Enseignement Sup - Mathématiques, EDP Sciences, 2011.
  11. Thermodynamic Formalism and Applications to Dimension Theory, Progress in Mathematics 294, Birkhäuser, 2011.
  12. Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, Universitext, Springer, 2012.
  13. (with C. Valls) Complex Analysis and Differential Equations, SUMS, Springer, 2012.
  14. Análisis Complejo y Ecuaciones Diferenciales, Delta Publicaciones, 2012.
  15. (with C. Valls) Ejercicios de Análisis Complejo y Ecuaciones Diferenciales, Delta Publicaciones, 2012.
  16. (with C. Valls) Sistemas Dinâmicos: Uma Introdução, Colecção Ensino da Ciência e da Tecnologia 44, IST Press, 2012.
  17. (with C. Valls) Ordinary Differential Equations: Qualitative Theory, Graduate Studies in Mathematics 137, American Mathematical Society, 2012.

Books as editor

  1. Special Issue Dedicated to Yakov Pesin on the Occasion of his 60th Birthday, Discrete Contin. Dyn. Syst. 22 (2008), 1-464.

Surveys

  1. Pesin theory, Encyclopaedia of Mathematics, Supplement I, Kluwer, 1997, pp. 406-411.
  2. (with Ya. Pesin) Lectures on Lyapunov exponents and smooth ergodic theory, with appendices by M. Brin and by D. Dolgopyat, H. Hu and Ya. Pesin, Smooth Ergodic Theory and Its Applications, Proc. Symposia Pure Math. 69, Amer. Math. Soc., 2001, pp. 3-106.
  3. Hyperbolicity and recurrence in dynamical systems: a survey of recent results, Resenhas IME-USP 5 (2002), 171-230.
  4. Hiperbolicidade, recorrência e dimensão, supplement to the Portuguese translation of Introduction to the Modern Theory of Dynamical Systems, Fundação Calouste Gulbenkian, 2005, pp. 665-724.
  5. Poincaré recurrence: old and new, XIV International Congress on Mathematical Physics (Lisboa, 2003), World Scientific, 2005, pp. 415-422.
  6. (with Ya. Pesin) Smooth ergodic theory and nonuniformly hyperbolic dynamics, with appendix by O. Sarig, Handbook of Dynamical Systems 1B, Elsevier, 2006, pp. 57-263.
  7. (with C. Valls) Stability in nonautonomous dynamics: a survey of recent results, São Paulo J. Math. Sci. 1 (2007), 133-174.
  8. Almost additive thermodynamic formalism: some recent developments, Rev. Math. Phys. 22 (2010), 1147-1179.
  9. (with K. Gelfert) Dimension estimates in smooth dynamics: a survey of recent results, Ergodic Theory Dynam. Systems 31 (2011), 641-671.

Selected Articles

  1. A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Ergodic Theory Dynam. Systems 16 (1996), 871-927.
  2. (with Ya. Pesin and J. Schmeling) On a general concept of multifractality: multifractal spectra for dimensions, entropies, and Lyapunov exponents. Multifractal rigidity, Chaos 7 (1997), 27-38.
  3. (with Ya. Pesin and J. Schmeling) Dimension and product structure of hyperbolic measures, Ann. of Math. (2) 149 (1999), 755-783.
  4. (with J. Schmeling) Sets of "non-typical" points have full topological entropy and full Hausdorff dimension, Israel J. Math. 116 (2000), 29-70.
  5. (with B. Saussol) Multifractal analysis of hyperbolic flows, Comm. Math. Phys. 214 (2000), 339-371.
  6. (with B. Saussol) Hausdorff dimension of measures via Poincaré recurrence, Comm. Math. Phys. 219 (2001), 443-463.
  7. (with B. Saussol) Variational principles and mixed multifractal spectra, Trans. Amer. Math. Soc. 353 (2001), 3919-3944.
  8. (with B. Saussol) Product structure of Poincaré recurrence, Ergodic Theory Dynam. Systems 22 (2002), 33-61.
  9. (with B. Saussol and J. Schmeling) Higher-dimensional multifractal analysis, J. Math. Pures Appl. 81 (2002), 67-91.
  10. (with C. Wolf) Measures of maximal dimension for hyperbolic diffeomorphisms, Comm. Math. Phys. 239 (2003), 93-113.
  11. (with P. Doutor) Birkhoff averages for hyperbolic flows: variational principles and applications, J. Stat. Phys. 115 (2004), 1567-1603.
  12. (with C. Silva) Lyapunov exponents for continuous transformations and dimension theory, Discrete Contin. Dyn. Syst. 13 (2005), 469-490.
  13. (with C. Valls) Smoothness of invariant manifolds for nonautonomous equations, Comm. Math. Phys. 259 (2005), 639-677.
  14. (with C. Valls) Stability of nonautonomous differential equations in Hilbert spaces, J. Differential Equations 217 (2005), 204-248.
  15. (with C. Valls) Center manifolds for nonuniformly partially hyperbolic diffeomorphisms, J. Math. Pures Appl. 84 (2005), 1693-1715.
  16. Nonadditive thermodynamic formalism: equilibrium and Gibbs measures, Discrete Contin. Dyn. Syst. 16 (2006), 279-305.
  17. (with C. Wolf) Pointwise dimension and ergodic decompositions, Ergodic Theory Dynam. Systems 26 (2006), 653-671.
  18. (with C. Valls) Multifractal structure of two-dimensional horseshoes, Comm. Math. Phys. 266 (2006), 455-470.
  19. (with C. Valls) A Grobman-Hartman theorem for nonuniformly hyperbolic dynamics, J. Differential Equations 228 (2006), 285-310.
  20. (with K. Gelfert) Multifractal analysis for Lyapunov exponents on nonconformal repellers, Comm. Math. Phys. 267 (2006), 393-418.
  21. (with G. Iommi) Suspension flows over countable Markov shifts, J. Statist. Phys. 124 (2006), 207-230.
  22. (with C. Valls) Nonuniform exponential dichotomies and Lyapunov regularity, J. Dynam. Differential Equations 19 (2007), 215-241.
  23. (with C. Valls) Hölder Grobman-Hartman linearization, Discrete Contin. Dyn. Syst. 18 (2007), 187-197.
  24. (with C. Valls) Conjugacies for linear and nonlinear perturbations of nonuniform behavior, J. Funct. Anal. 253 (2007), 324-358.
  25. (with V. Saraiva) Multifractal nonrigidity of topological Markov chains, J. Statist. Phys. 130 (2008), 387-412.
  26. (with C. Valls) Robustness of nonuniform exponential dichotomies in Banach spaces, J. Differential Equations 244 (2008), 2407-2447.
  27. (with C. Valls) Analytic invariant manifolds for sequences of diffeomorphisms, J. Differential Equations 245 (2008), 80-101.
  28. (with C. Valls) Growth rates and nonuniform hyperbolicity, Discrete Contin. Dyn. Syst. 22 (2008), 509-528.
  29. (with G. Iommi) Partial quotients of continued fractions and $\beta$-expansions, Nonlinearity 21 (2008), 2211-2219.
  30. (with C. Valls) Lyapunov sequences for exponential dichotomies, J. Differential Equations 246 (2009), 183-215.
  31. (with C. Valls) Quadratic Lyapunov functions and nonuniform exponential dichotomies, J. Differential Equations 246 (2009), 1235-1263.
  32. (with G. Iommi) Frequency of digits in the Lüroth expansion, J. Number Theory 129 (2009), 1479-1490.
  33. (with P. Doutor) Almost additive multifractal analysis, J. Math. Pures Appl. 92 (2009), 1-17.
  34. (with C. Valls) Robustness of discrete dynamics via Lyapunov sequences, Comm. Math. Phys. 290 (2009), 219-238.
  35. (with P. Doutor) Dimension spectra of hyperbolic flows, J. Statist. Phys. 136 (2009), 505-525.
  36. (with J. Llibre and C. Valls) Periodic orbits near equilibria, Comm. Pure Appl. Math. 63 (2010), 1225-1236.
  37. (with C. Valls) Admissibility for nonuniform exponential contractions, J. Differential Equations 249 (2010), 2889-2904.
  38. (with J. Llibre and C. Valls) On a degenerate Hopf bifurcation, J. Phys. A 43 (2010), no. 28, 285201, 14 pp.
  39. (with G. Iommi) Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes, Israel J. Math. 181 (2011), 347-379.
  40. (with C. Valls) Smooth robustness of exponential dichotomies, Proc. Amer. Math. Soc. 139 (2011), 999-1012.