Jairo Bochi

Associate Professor
Facultad de Matemáticas, PUC-Chile

“In Mathematics, unlike elsewhere, wrong notions die off easily. Our capacity for understanding is hampered, foremost, by the inability to dispel false concepts.” – Alexander Beilinson

About me:

I am a mathematician. I completed my undergraduate studies at UFRGS (Porto Alegre, Brazil) in 1996, and my PhD at IMPA (Rio de Janeiro, Brazil) in 2001. I have previsouly had tenured positions on UFRGS and PUC-Rio. I arrived at PUC-Chile in 2014. My research focuses on Dynamical Systems and its relations to Geometry, Linear Algebra, and Control Theory.

Curriculum Vitae pdf

Facultad de Matemáticas
Pontificia Universidad Católica de Chile (PUC-Chile)
Av. Vicuña Mackenna #4860, Macul
Santiago - Chile
Office: 322
Phone: +56(02)2354-1025
Email: email


2018/2 Sistemas Dinámicos (MAT2565) 2015/1 -
2017/2 Teoría Ergódica (MPG3960), Precálculo (MAT1000) 2017/1 Cálculo I (MAT1610)
2016/2 Cálculo I (MAT1610) 2016/1 Análisis Real (MAT2515), Variable Compleja (MPG3950)
2015/2 Sistemas Dinámicos (MAT2565), Cálculo III (MAT1630) 2015/1 Teoría de Integración (MAT2535)
2014/2 Cálculo II (MAT220E) 2014/1 Geometría Diferencial (MAT2305)

Research papers:

Title Joint with... “Slides”   Published in ... Link/File
Ergodic optimization of Birkhoff averages and Lyapunov exponents - To appear in Proceedings of the International Congress of Mathematicians, Rio de Janeiro 2018 arxiv
Equilibrium states of generalised singular value potentials and applications to affine iterated function systems Ian D. Morris Submitted hourglass arxiv
Dominated Pesin theory: convex sum of hyperbolic measures Christian Bonatti, Katrin Gelfert To appear in Israel Journal of Mathematics arxiv
On the approximation of convex bodies by ellipses with respect to the symmetric difference metric - Submitted hourglass arxiv
Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases M. Bessa, M. Cambrainha, C. Matheus, P. Varandas, Disheng Xu Bulletin of the Brazilian Mathematical Society doi link / arxiv
A criterion for zero averages and full support of ergodic measures Christian Bonatti, Lorenzo J. Díaz To appear in Moscow Mathematical Journal arxiv
Anosov representations and dominated splittings Rafael Potrie, Andrés Sambarino pdf To appear in Journal of the European Mathematical Society arxiv
The Lyapunov spectra of fiber-bunched cocycles (working title) Clark Butler In progress... work
Flexibility of Lyapunov exponents among conservative diffeormophisms (working title) Anatole Katok, Federico Rodriguez Hertz pdf In progress... work
Extremal norms for fiber-bunched cocycles (working title) Eduardo Garibaldi In progress... work
Robust criterion for the existence of nonhyperbolic measures Christian Bonatti, Lorenzo J. Díaz Communications in Mathematical Physics 344 (2016), no. 3, pp. 751-795. doi link / arxiv
The scaling mean and a law of large permanents Godofredo Iommi, Mario Ponce Advances in Mathematics 292 (2016), pp. 374-409. doi link / arxiv
Ergodic optimization of prevalent super-continuous functions Yiwei Zhang pdf International Mathematics Research Notices 2016 (2016), no. 19, pp. 5988-6017. doi link / arxiv
Cocycles of isometries and denseness of domination - Quarterly Journal of Mathematics 66 (2015), no. 3, pp. 773-798. doi link / arxiv
Peano curves with smooth footprints Pedro H. Milet Monatshefte für Mathematik 180 (2016), no. 4, pp. 693-712. doi link / arxiv
The entropy of Lyapunov-optimizing measures of some matrix cocycles Michał Rams pdf Journal of Modern Dynamics 10 (2016), pp. 255-286. doi link / arxiv
Continuity properties of the lower spectral radius Ian D. Morris Proceedings of the London Mathematical Society 110 (2015), pp. 477-509. doi link / arxiv
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 Annales de l'Institut Henri Poincaré - analyse non linéaire 31 (2014), no. 6, pp. 1101-1107. doi link / arxiv
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 Mathematics of Control, Signals, and Systems 26 (2014), no. 4, pp. 481-518. doi link / arxiv
A geometric path from zero Lyapunov exponents to rotation cocycles Andrés Navas pdf Ergodic Theory and Dynamical Systems 35 (2015), no. 2, pp. 374-402. 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 Correction: 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. link / 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
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. link / pdf
Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure Artur Avila Mathematical Research Letters 14 (2007), no. 5, 721-730. doi link / 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 (2006), 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. doi link / 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

Notes and other texts:




Scientific service:

I'm a member of the editorial board of Discrete and Continuous Dynamical Systems - Series A.

I was one of the organizers of the EDAI Dynamical Systems Seminar for a few years.

Some math-related bookmarks:

My profiles: AMS MathSciNet   Researchgate   Researchgate   Math Genealogy   MathOverflow

chalkboard Colloquium of PUC-Chile math department chalkboard Santiago Dynamical Systems seminar Chile flag Dynamical Systems in Chile
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
IMU logo Proceedings of the ICM's 1893-2010 book GDZ database book AMS Open Math Notes
book Allen Hatcher's (free!) Algebraic Topology book video icon Mathematical English Usage Dictionary Origin of some words in Mathematics
rook Hyperbolic maze (a game) Square peg problem (applet) video icon Funny MathReviews

Personal stuff:

Checking in at Hilbert's My favorite superhero

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