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Jairo da Silva Bochi

Associate professor

PUC-Chile

Santiago, Chile

Líneas de Investigación


Dynamical systems

Educación

  •  Dynamical systems, IMPA. Brasil, 2001

Experiencia Académica

  •   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 - At present

Formación de Capital Humano


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


Difusión y Transferencia


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".


Premios y Distinciones

  •   Affiliate Member

    Brazilian Academy of Sciences

    Brasil, 2008

    Affiliate member of the Brazilian Academy of Sciences


 

Article (31)

Peano curves with smooth footprints
Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures
THE ENTROPY OF LYAPUNOV-OPTIMIZING MEASURES OF SOME MATRIX COCYCLES
The scaling mean and a Law of Large Permanents
A geometric path from zero Lyapunov exponents to rotation cocycles
COCYCLES OF ISOMETRIES AND DENSENESS OF DOMINATION
Continuity properties of the lower spectral radius
Ergodic Optimization of Prevalent Super-continuous Functions
Almost reduction and perturbation of matrix cocycles
Robust vanishing of all Lyapunov exponents for iterated function systems
Universal regular control for generic semilinear systems
Generic linear cocycles over a minimal base
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms
Opening gaps in the spectrum of strictly ergodic Schr?dinger operators
Perturbation of the Lyapunov spectra of periodic orbits
C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents
Uniformly hyperbolic finite-valued SL(2,?)-cocycles
Cantor spectrum for Schr?dinger operators with potentials arising from generalized skew-shifts
Nonuniform center bunching and the genericity of ergodicity among C1 partially hyperbolic symplectomorphisms
Some characterizations of domination
A uniform dichotomy for generic SL(2,R) cocycles over a minimal base
Generic expanding maps without absolutely continuous invariant $\sigma$-finite measure
A generic C 1 map has no absolutely continuous invariant probability measure
A remark on conservative diffeomorphisms
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for SL(2, ?) cocycles
The Lyapunov exponents of generic volume-preserving and symplectic maps
Inequalities for numerical invariants of sets of matrices
L p -GENERIC COCYCLES HAVE ONE-POINT LYAPUNOV SPECTRUM
A formula with some applications to the theory of Lyapunov exponents
Genericity of zero Lyapunov exponents
Uniform (projective) hyperbolicity or no hyperbolicity: A dichotomy for generic conservative maps

Proyecto (2)

Geometrical aspects of multiplicative ergodic theory
Center for Dynamical Systems and Related Topics
33
Jairo Bochi

Associate professor

Mathematics

PUC-Chile

Santiago, Chile

2
Andres Navas

Full time Professor

Mathematics

DPTO DE MATEMATICA Y CC, USACH

Santiago, Chile

1
Godofredo Iommi

Profesor Asociado

Facultad de Matemáticas

Pontificia Universidad Catolica de Chile

Santigo, Chile

1
Mario Ponce

Dean

Mathematics

Pontificia Universidad Católica de Chile

Santiago, Chile