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Jairo da Silva Bochi

Associate professor

PUC-Chile

Santiago, Chile

Dynamical systems

Dynamical systems, IMPA. Brasil, 2001

Assistant professor Full Time

UFRGS

Porto Alegre, Brasil

2005 - 2007
Assistant professor Full Time

PUC-Rio

Rio de Janeiro, Brasil

2008 - 2011
Associate professor Full Time

PUC-Rio

Rio de Janeiro, Chile

2011 - 2013
Associate professor Full Time

PUC-Chile

Mathematics

Santiago, Chile

2014 - A la fecha

CURRENT STUDENTS:
Eduardo Camilo Oregón Reyes. Magíster
Renato Adolfo Velozo Ruiz. Magíster

PREVIOUS STUDENTS:
Paulo N. Orenstein, co-advised by Carlos Tomei. MSc dissertation (Jan 23, 2014): Optimal transport and the Wasserstein metric.
Cong Zhou. MSc dissertation (Mar 11, 2013): Multiplicative ergodic theorem in non-positively curved spaces.
Miguel K. Schnoor. PhD thesis (Aug 3, 2012): The non-existence of absolutely continuous invariant probabilities is C1-generic for flows.
Pedro Henrique Milet P. Pereira. MSc dissertation (Mar 25, 2011): Peano curves and line fields

Coordinación del Taller de Investigación Matemática (TIM) para alumnos de enseñanza media.

Diciembre 2016: charla en el SUMA 2016 (Primer encuentro conjunto de la Sociedad de Matemática de Chile y la Unión Matemática Argentina), Valparaíso, Chile. Título de la charla: "Flexibility of Lyapunov Exponents".

Agosto 2015: charla en el congresso Global Dynamics Beyond Uniform Hyperbolicity 2015, Olmué, Chile. Título de la charla: "Linear representations and dominated splittings".

Julio 2015: charla en el Oberwolfach Dynamical Systems Workshop, Oberwolfach, Alemania. Título de la charla: "Linear representations and dominated splittings".

Junio 2015: charla en el Third Palis-Balzan Symposium on Dynamical Systems, Paris, Francia. Título de la charla: "Ergodic optimization and prevalence".

Enero 2015: Charla en el congreso Random Dynamical Systems and Multiplicative Ergodic Theorems, Banff, Canada. Título de la charla: "Optimization of Lyapunov exponents of matrix cocycles".

Octubre 2014: Charla en la III Escola Brasileira de Sistemas Dinâmicos, Bento Gonçalves, Brasil. Título de la charla: "The law of large permanents".

Abril 2014: Charla en el Chapel Hill Ergodic Theory Workshop, Chapel Hill, EE.UU. Título de la charla: "Optimization of Lyapunov exponents of matrix cocycles".

Affiliate Member

Brazilian Academy of Sciences

Brasil, 2008

Affiliate member of the Brazilian Academy of Sciences


Peano curves with smooth footprints Bochi, J; Milet P.H. Article ISI SCOPUS Monatshefte fur Mathematik (2016)
Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures Bochi, J; Bonatti, C; Díaz L.J. Article ISI SCOPUS Communications in Mathematical Physics (2016)
The entropy of Lyapunov-optimizing measures of some matrix cocycles Bochi, Jairo; Rams, Michal Article ISI SCOPUS JOURNAL OF MODERN DYNAMICS (2016)
The scaling mean and a Law of Large Permanents Bochi, Jairo; Iommi, Godofredo; Ponce, Mario Article ISI SCOPUS Advances in Mathematics (2016)
A geometric path from zero Lyapunov exponents to rotation cocycles Bochi, Jairo; Navas, Andres Article ISI SCOPUS Ergodic Theory and Dynamical Systems (2015)
COCYCLES OF ISOMETRIES AND DENSENESS OF DOMINATION Bochi, J Article ISI SCOPUS Quarterly Journal of Mathematics (2015)
Continuity properties of the lower spectral radius Bochi, J; Morris, ID Article ISI SCOPUS Proceedings of the London Mathematical Society (2015)
Ergodic Optimization of Prevalent Super-continuous Functions Bochi, Jairo; Zhang, Yiwei Article International Mathematics Research Notices (2015)
Almost reduction and perturbation of matrix cocycles Bochi, J; Navas A. Article ISI SCOPUS ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2014)
Robust vanishing of all Lyapunov exponents for iterated function systems Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J. Article MATHEMATISCHE ZEITSCHRIFT (2014)
Universal regular control for generic semilinear systems Bochi, J; Gourmelon, N Article MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS (2014)
Generic linear cocycles over a minimal base Bochi, Jairo Article Studia Mathematica (2013)
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms Avila, Artur; Bochi, Jairo Article TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2012)
Opening gaps in the spectrum of strictly ergodic Schr?dinger operators Avila, Artur; Bochi, Jairo; Damanik, David Article JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2012)
Perturbation of the Lyapunov spectra of periodic orbits Bochi, J.; Bonatti, C. Article Proceedings of the London Mathematical Society (2012)
C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents Bochi, Jairo Article Journal of the Institute of Mathematics of Jussieu (2010)
Uniformly hyperbolic finite-valued SL(2,?)-cocycles Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe Article Commentarii Mathematici Helvetici (2010)
Cantor spectrum for Schr?dinger operators with potentials arising from generalized skew-shifts Avila, Artur; Bochi, Jairo; Damanik, David Article DUKE MATHEMATICAL JOURNAL (2009)
Nonuniform center bunching and the genericity of ergodicity among C1 partially hyperbolic symplectomorphisms Avila, A.; Bochi, J.; Wilkinson, A. Article ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE (2009)
Some characterizations of domination Bochi, Jairo; Gourmelon, Nicolas Article MATHEMATISCHE ZEITSCHRIFT (2009)
A uniform dichotomy for generic SL(2,R) cocycles over a minimal base Avila, A.; Bochi, J. Article BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE (2007)
Generic expanding maps without absolutely continuous invariant $\sigma$-finite measure Avila, Artur; Bochi, Jairo Article Mathematical Research Letters (2007)
A generic C 1 map has no absolutely continuous invariant probability measure Avila, Artur; Bochi, Jairo Article Nonlinearity (2006)
A remark on conservative diffeomorphisms Bochi, Jairo; Fayad, Bassam R.; Pujals, Enrique Article Comptes Rendus Mathematique (2006)
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for SL(2, ?) cocycles Bochi*, Jairo; Fayad, Bassam Article Bulletin of the Brazilian Mathematical Society, New Series (2006)
The Lyapunov exponents of generic volume-preserving and symplectic maps Bochi, Jairo; Viana, Marcelo Article Annals of Mathematics (2005)
Inequalities for numerical invariants of sets of matrices Bochi, Jairo Article Linear Algebra and its Applications (2003)
L p -GENERIC COCYCLES HAVE ONE-POINT LYAPUNOV SPECTRUM ARBIETO, ALEXANDER; Bochi, Jairo Article Stochastics and Dynamics (2003)
A formula with some applications to the theory of Lyapunov exponents Avila, Artur; Bochi, Jairo Article ISRAEL JOURNAL OF MATHEMATICS (2002)
Genericity of zero Lyapunov exponents Bochi, Jairo Article Ergodic Theory and Dynamical Systems (2002)
Uniform (projective) hyperbolicity or no hyperbolicity: A dichotomy for generic conservative maps Bochi, Jairo; Viana, Marcelo Article Annales de l'Institut Henri Poincaré C, Analyse non linéaire (2002)


Geometrical aspects of multiplicative ergodic theory Bochi, Jairo Proyecto (2014)
Center for Dynamical Systems and Related Topics Navas, Andrés; Cortez, María Isabel; Iommi, Godofredo; Vasquez, Carlos; Schraudner, Michael; Bochi, Jairo Proyecto (2013)