Jairo Bochi

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:

Some papers (newest first):

Title (click over it for the abstract)	Joint with...	Published in ...	Link/File
Perturbation of the Lyapunov spectrum of periodic orbits (working title)	Christian Bonatti	In progress...
A $C^1$-generic dichotomy for volume-preserving diffeomorphisms: global dominated splitting or zero exponent almost everywhere (working title)	Artur Avila	In progress...
Opening gaps in the spectrum of strictly ergodic Schrödinger operators	Artur Avila and David Damanik	Submitted
Nonuniform center bunching and the genericity of ergodicity among $C^1$ partially hyperbolic symplectomorphisms	Artur Avila and Amie Wilkinson	To appear in Annales Scientifiques de l'École Normale Supérieure
Some characterizations of domination	Nicolas Gourmelon	Mathematische Zeitschrift, 263, no. 1 (2009), 221-231.	/
Uniformly hyperbolic finite-valued $SL(2,R)$ cocycles	Artur Avila and Jean-Christophe Yoccoz	To appear in Commentarii Mathematici Helvetici
$C^1$-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents	-	To appear in Journal of the Institute of Mathematics of Jussieu	/
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts	Artur Avila and 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 $SL(2,R)$ 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 $SL(2,R)$ cocycles	Bassam Fayad	Bulletin of the Brazilian Mathematical Society, 37, no. 3 (2006), 307-349.	/
A remark on conservative diffeomorphisms	Bassam Fayad and 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 and 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	,

Lecture notes etc:

• A métrica projetiva de Hilbert: texto (de Paulo Orenstein) ; programa para visualizar (de Frederico Israel): executável Windows, instruções, fonte Linux.
• 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:

Official Curriculum (Currículo Lattes)

Other links:

Allen Hatcher's (free!) Algebraic Topology book

EDAÍ Dynamical Systems Seminar

Last update: September, 2009.