Jairo Bochi Professor associado Departamento de Matemática, PUC-Rio

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.

Currículo Lattes = Official CV

Endereço = Address: Departamento de Matemática PUC-Rio Rua Marquês de São Vicente, 225 22453-900 Rio de Janeiro, RJ - Brasil

Sala: L749 Telefone: (21) 3527-1722 Email:

Ensino = Teaching:

Research papers:

Here is a commented list:

Title	Joint with...	“Slides”	Published in ...	Link/File
Universal regular control for generic semilinear systems	Nicolas Gourmelon		...
A geometric path form zero Lyapunov exponents to rotation cocycles	Andrés Navas		Submitted...
Robust vanishing of all central Lyapunov exponents (working title)	Christian Bonatti, Lorenzo J. Díaz		In progress...
Perturbation of the Lyapunov spectra of periodic orbits	Christian Bonatti		To appear in Proceedings of the London Mathematical Society
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms	Artur Avila		To appear in Transactions of the American Mathematical Society
Opening gaps in the spectrum of strictly ergodic Schrödinger operators	Artur Avila, David Damanik		Journal of the European Mathematical Society, 14, no. 1 (2012), 61-106	/
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, n. 6 (2009), 931-979
Some characterizations of domination	Nicolas Gourmelon		Mathematische Zeitschrift, 263, no. 1 (2009), 221-231.	/
Uniformly hyperbolic finite-valued \({\rm SL}(2,\Bbb{R})\) cocycles	Artur Avila, Jean-Christophe Yoccoz		Commentarii Mathematici Helvetici, 85, no. 4 (2010), 813-884.	/
\(C^1\)-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents	-		Journal of the Institute of Mathematics of Jussieu, 9, no. 1 (2010), 49-93.	/
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts	Artur Avila, David Damanik		Duke Mathematical Journal, 146, no. 2 (2009), 253-280.	/
Cocycles over generic volume preserving dynamics (working title)	Nicolas Gourmelon		In progress...
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.
Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure	Artur Avila		Mathematical Research Letters 14 (2007), 721-730.
A generic \(C^1\) map has no absolutely continuous invariant probability measure	Artur Avila		Nonlinearity 19 (2006), 2717-2725.	/
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for \({\rm SL}(2,\Bbb{R})\) cocycles	Bassam Fayad		Bulletin of the Brazilian Mathematical Society, 37, no. 3 (2006), 307-349.	/
A remark on conservative diffeomorphisms	Bassam Fayad, Enrique Pujals		Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), 763-766.	/
\(L^p\)-generic cocycles have one-point Lyapunov spectrum	Alexander Arbieto		Stochastics and Dynamics, 3 (2003), 73-81. Corrigendum. ibid, 3 (2003), 419-420.	/ +
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.
Inequalities for numerical invariants of sets of matrices	-		Linear Algebra and its Applications, 368 (2003), 71-81.	/
The Lyapunov exponents of generic volume preserving and symplectic maps	Marcelo Viana		Annals of Mathematics, 161 (2005), No. 3, 1423--1485.
Robust transitivity and topological mixing for \(C^1\)-flows	Flavio Abdenur, Artur Avila		Proceedings of American Mathematical Society, 132 (2004), 699-705.	/
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.	/
A formula with some applications to the theory of Lyapunov exponents	Artur Avila		Israel Journal of Mathematics, 131 (2002), 125-137.	/
Genericity of zero Lyapunov exponents	-		Ergodic Theory and Dynamical Systems, 22 (2002), 1667-1696.	/ ,
Discontinuity of the Lyapunov exponent for non-hyperbolic cocycles	-		Not intended for publication	,

Other texts: Lecture notes, other talks etc:

• Note on the dimension of certain algebraic sets of matrices (with N. Gourmelon):
• Geometria muito além dos gregos (palestra para os calouros):
• Médias aritméticas disfarçadas (palestra Oktobermat):
• Proof of the subadditive ergodic theorem (with A. Avila):
• Notes of the course on Lyapunov exponents given at the Workshop on D.S. at Trieste, with A. Avila: First week:; second week: (manuscript by Aline Cerqueira).
• Notes on a theorem of Furstenberg on random products of matrices:
• Proofs of Oseledets theorem: In dimension 2 via hyperbolic geometry: . In any dimension :
• Dois espaços compactos contráteis com um ponto em comum cuja união não é contrátil (seguindo Elon L. Lima):
• Raízes de polinômios com coeficientes inteiros limitados:

Alunos = Students:

Atuais = Current:

• Miguel K. Schnoor (doutorado; bolsa CNPq). Projeto: Campos de vetores e medidas absolutamente contínuas.
• Leonardo Lobo C. da Fontoura, Frederico B. Israel (iniciação científica; bolsa CNPq). Projeto: A geometria dos rastros de bicicleta.

Prévios = Former:

• Pedro Henrique Milet P. Pereira (mestrado; bolsa Faperj Nota 10). Dissertação: Curvas de Peano e campos de direções.
• Paulo Orenstein, Frederico B. Israel (iniciação científica). Projeto: A métrica projetiva de Hilbert. Texto (de Paulo Orenstein) ; programa para visualizar (de Frederico Israel): executável Windows, instruções, fonte Linux.

Some math-related bookmarks:

Oktobermat	EDAÍ Dynamical Systems Seminar
Allen Hatcher's (free!) Algebraic Topology book	GDZ database
Feynman's Messenger Lectures on Project Tuva	Origin of some words in Mathematics

Personal stuff:

Last update: January, 2012.