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Jairo Bochi

Professor associado
Departamento de Matemática, PUC-Rio
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Sobre mim = About me:

Cursei graduação (93-96) e mestrado (96-97) na UFRGS, e doutorado (97-01) no IMPA. Sou professor do Departamento de Matemática da PUC-Rio desde 2008. Minha pesquisa se concentra em Sistemas Dinâmicos.

I completed my undergraduate studies at UFRGS (1996), and my PhD at IMPA (2001). I'm a professor at PUC-Rio since 2008. My research focuses on Dynamical Systems.

Curriculum Vitae pdf Currículo Lattes = Official CV

Endereço = Address:
Departamento de Matemática
Rua Marquês de São Vicente, 225
22451-900 Rio de Janeiro, RJ - Brasil
Sala: L849
Telefone: (21) 3527-1756
Email: email.gif

Ensino = Teaching:

2013/2 Medida e Integração (MAT2621), Seminário de Sistemas Dinâmicos (MAT2936)
2013/1 Matemática Discreta (MAT1310), Introdução à Análise (MAT1605)
2012/2 Álgebra Linear I (MAT1200), Teoria Ergódica.
2012/1 Cálculo a Várias Variáveis I (MAT1162), Introdução à Probabilidade (MAT1413)
2011/2 Introdução à Análise (MAT1605), Variedades Diferenciáveis (MAT2821)
2011/1 Equações Diferenciais e de Diferenças (MAT1154), Medida e Integração (MAT2621)
2010/2 Equações Diferenciais e de Diferenças (MAT1154), Análise no \(\Bbb{R}^n\) (MAT1612)
2010/1 Matemática Discreta (MAT1310), Introdução à Probabilidade (MAT1413)
2009/2 Matemática Discreta (MAT1310), Introdução à Análise (MAT1605)
2009/1 Cálculo a Várias Variáveis I (MAT1162), Seminário de Dinâmica
2008/2 Cálculo Diferencial de Várias Variáveis (MAT1152), Introdução à Dinâmica: Dimensão 1
2008/1 Álgebra Linear I (MAT1200)

Research papers:

Here is a commented list: pdf
Title Joint with... “Slides”   Published in ... Link/File
The entropy of Lyapunov-optimizing measures of some matrix cocycles Michał Rams pdf Submitted arxiv
Continuity properties of the lower spectral radius Ian D. Morris Submitted arxiv
Robust criteria for the existence of nonhyperbolic measures (working title) Christian Bonatti, Lorenzo J. Díaz In progress... work
Generic linear cocycles over a minimal base - Studia Mathematica, 218 (2013), no. 2, pp. 167-188. doi link / arxiv
Almost reduction and perturbation of matrix cocycles Andrés Navas To appear in Annales de l'Institut Henri Poincaré - Analyse Non Linéaire. doi link / arxiv
Denseness of domination (working title) - In progress... work
Robust vanishing of all Lyapunov exponents for iterated function systems Christian Bonatti, Lorenzo J. Díaz Mathematische Zeitschrift 176 (2014), pp. 469-503. doi link / arxiv
Universal regular control for generic semilinear systems Nicolas Gourmelon pdf ... arxiv
A geometric path from zero Lyapunov exponents to rotation cocycles Andrés Navas pdf To appear in Ergodic Theory and Dynamical Systems. doi link / pdf
Perturbation of the Lyapunov spectra of periodic orbits Christian Bonatti pdf Proceedings of the London Mathematical Society 105 (2012), no. 1, pp. 1-48. doi link / pdf
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms Artur Avila Transactions of the American Mathematical Society 364 (2012), no. 6, pp. 2883-2907. doi link / pdf
Opening gaps in the spectrum of strictly ergodic Schrödinger operators Artur Avila, David Damanik Journal of the European Mathematical Society 14 (2012), no. 1, pp. 61-106 doi link / pdf
Nonuniform center bunching and the genericity of ergodicity among \(C^1\) partially hyperbolic symplectomorphisms Artur Avila, Amie Wilkinson Annales Scientifiques de l'École Normale Supérieure 42 (2009), no. 6, pp. 931-979. pdf
Some characterizations of domination Nicolas Gourmelon Mathematische Zeitschrift 263 (2009), no. 1, pp. 221-231. doi link / arxiv
Uniformly hyperbolic finite-valued \({\rm SL}(2,\Bbb{R})\) cocycles Artur Avila, Jean-Christophe Yoccoz Commentarii Mathematici Helvetici 85 (2010), no. 4, pp. 813-884. doi link / pdf
\(C^1\)-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents - pdf Journal of the Institute of Mathematics of Jussieu, 9 (2010), no. 1, pp. 49-93. doi link / pdf
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts Artur Avila, David Damanik Duke Mathematical Journal 146 (2009), no. 2, pp. 253-280. doi link / pdf
Cocycles over generic volume preserving dynamics (working title) Nicolas Gourmelon In progress... work
A uniform dichotomy for generic \({\rm SL}(2,\Bbb{R})\) cocycles over a minimal base Artur Avila Bulletin de la Société Mathématique de France 135 (2007), 407--417. pdf
Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure Artur Avila Mathematical Research Letters 14 (2007), 721-730. pdf
A generic \(C^1\) map has no absolutely continuous invariant probability measure Artur Avila Nonlinearity 19 (2006), 2717-2725. doi link / pdf
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for \({\rm SL}(2,\Bbb{R})\) cocycles Bassam Fayad Bulletin of the Brazilian Mathematical Society 37 (2003), no. 3, 307-349. doi link / pdf
A remark on conservative diffeomorphisms Bassam Fayad, Enrique Pujals Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), 763-766. doi link / pdf
\(L^p\)-generic cocycles have one-point Lyapunov spectrum Alexander Arbieto Stochastics and Dynamics 3 (2003), 73-81. Corrigendum. ibid, 3 (2003), 419-420. doi link / pdf + pdf
Lyapunov exponents: How frequently are dynamical systems hyperbolic? Marcelo Viana Modern dynamical systems and applications, 271-297, Brin, Hasselblatt, Pesin (eds.) Cambridge Univ. Press, 2004. pdf
Inequalities for numerical invariants of sets of matrices - Linear Algebra and its Applications, 368 (2003), 71-81. doi link / pdf
The Lyapunov exponents of generic volume preserving and symplectic maps Marcelo Viana Annals of Mathematics, 161 (2005), No. 3, 1423--1485. pdf
Robust transitivity and topological mixing for \(C^1\)-flows Flavio Abdenur, Artur Avila Proceedings of American Mathematical Society, 132 (2004), 699-705. doi link / pdf
Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps Marcelo Viana Annales de l'Institut Henri Poincaré - Analyse non linéaire, 19 (2002), 113-123. doi link / pdf
A formula with some applications to the theory of Lyapunov exponents Artur Avila Israel Journal of Mathematics, 131 (2002), 125-137. doi link / pdf
Genericity of zero Lyapunov exponents - Ergodic Theory and Dynamical Systems, 22 (2002), 1667-1696. doi link / ps, pdf
Discontinuity of the Lyapunov exponent for non-hyperbolic cocycles - Permanent preprint ps, pdf

AMS My profile on MathSciNet Google My profile on Google Scholar

Other texts: Lecture notes, other talks etc:

Alunos = Students:

Prévios = Former:

Some math-related bookmarks:

faixa EDAI EDAÍ Dynamical Systems Seminar dinamicarioca DinamiCarioca beer mug Oktobermat
video icon Mathematical Imagery by Jos Leys video icon Videos of talks in Dynamical Systems (CUNY Einstein Chair Math. Seminar) video icon Feynman's Messenger Lectures on Project Tuva
GDZ database Mathematical English Usage - Online Dictionary Origin of some words in Mathematics
book Allen Hatcher's (free!) Algebraic Topology book

Personal stuff:

Checking in at Hilbert's My favorite superhero Look around you

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