
“It is, first and foremost, characteristic of human beings to seek and probe for the truth. And so when we are free from mandatory duties and concerns we are keen to see, hear, and learn things and we think that knowledge of arcane or wondrous things is indispensable for the happy life. From this we can conclude that whatever is true, simple, and pure is most suited to human nature.” – Cicero, De Officiis (translation by Brad Inwood)
“Who but a barbarian could fail to believe that a man cannot stand alone if he wishes to create, that tradition is actually the precondition of creation, not its antithesis?” – Theodore Dalrymple
“Mathematics knows no races or geographic boundaries; for Mathematics, the cultural world is one country.” – David Hilbert
“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
“The beauty of mathematics lies in uncovering the hidden simplicity and complexity that coexist in the rigid logical framework that the subject imposes.” – David Ruelle
“La Mathématique est l’art de donner le même nom à des choses différentes.” – Henri Poincaré
My research focuses on Dynamical Systems and its relations to Geometry, Linear Algebra, and Control Theory. I completed my PhD at IMPA (Brazil) in 2001. I have previsouly worked at UFRGS (Brazil), PUCRio (Brazil), and PUCChile. I came to Penn State in 2021. I'm a member of the Anatole Katok Center for Dynamical Systems and Geometry.


Spring 2025: Ergodic Theory (Math 506)
Fall 2024: Real Analysis (Math 501)
Spring 2024: Classical Analysis II (Math 404)
Fall 2023: Real Analysis (Math 501)
Spring 2023: Complex Analysis (Math 502)
Fall 2022: Honors Concepts of Discrete Mathematics (Math 311M)
Spring 2022: Classical Analysis I (Math 403)
Fall 2021: Dynamical Systems II (Math 508)
Title  Joint with...  “Slides”  Published in ...  Link/File 

Hypergeometric means and their completion (working title)    ...  
Spectrum maximizing products are not generically unique  Piotr Laskawiec  SIAM Journal on Matrix Analysis and Applications, 45 (2024), no. 1, pp. 585600.  /  
The HalászSzékely barycenter  Godofredo Iommi, Mario Ponce  Proceedings of the Edinburgh Mathematical Society, 65 (2022), pp. 881911.  /  
Flexibility of Lyapunov exponents  Anatole Katok, Federico Rodriguez Hertz  Ergodic Theory and Dynamical Systems, 42 (2022), pp. 554591.  /  
On emergence and complexity of ergodic decompositions  Pierre Berger  Advances in Mathematics, 390 (2021), 107904.  /  
Extremal norms for fiber bunched cocycles  Eduardo Garibaldi  Journal de l'École polytechnique  Mathématiques, 6 (2019), pp. 9471004.  /  
Ergodic optimization of Birkhoff averages and Lyapunov exponents    Proceedings of the International Congress of Mathematicians 2018, Rio de Janeiro, vol. 2, pp. 18211842.  / /  
Equilibrium states of generalised singular value potentials and applications to affine iterated function systems  Ian D. Morris  Geometric and Functional Analysis, 28 (2018), no. 4, pp. 9951028.  /  
Dominated Pesin theory: convex sum of hyperbolic measures  Christian Bonatti, Katrin Gelfert  Israel Journal of Mathematics, 226 (2018), no. 1, pp. 387417.  /  
On the approximation of convex bodies by ellipses with respect to the symmetric difference metric    Discrete & Computational Geometry, 60 (2018), no. 4, pp. 938966.  /  
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, 49 (2018), no. 1, pp. 7387.  /  
A criterion for zero averages and full support of ergodic measures  Christian Bonatti, Lorenzo J. Díaz  Moscow Mathematical Journal, 18 (2018), no. 1, pp. 1561.  /  
Anosov representations and dominated splittings  Rafael Potrie, Andrés Sambarino  Journal of the European Mathematical Society 21 (2019), no. 11, pp. 33433414.  /  
Robust criterion for the existence of nonhyperbolic measures  Christian Bonatti, Lorenzo J. Díaz  Communications in Mathematical Physics 344 (2016), no. 3, pp. 751795.  /  
The scaling mean and a law of large permanents  Godofredo Iommi, Mario Ponce  Advances in Mathematics 292 (2016), pp. 374409.  /  
Ergodic optimization of prevalent supercontinuous functions  Yiwei Zhang  International Mathematics Research Notices 2016 (2016), no. 19, pp. 59886017.  /  
Cocycles of isometries and denseness of domination    Quarterly Journal of Mathematics 66 (2015), no. 3, pp. 773798.  /  
Peano curves with smooth footprints  Pedro H. Milet  Monatshefte für Mathematik 180 (2016), no. 4, pp. 693712.  /  
The entropy of Lyapunovoptimizing measures of some matrix cocycles  Michał Rams  Journal of Modern Dynamics 10 (2016), pp. 255286.  /  
Continuity properties of the lower spectral radius  Ian D. Morris  Proceedings of the London Mathematical Society 110 (2015), pp. 477509.  /  
Generic linear cocycles over a minimal base    Studia Mathematica 218 (2013), no. 2, pp. 167188.  /  
Almost reduction and perturbation of matrix cocycles  Andrés Navas  Annales de l'Institut Henri Poincaré  analyse non linéaire 31 (2014), no. 6, pp. 11011107.  /  
Robust vanishing of all Lyapunov exponents for iterated function systems  Christian Bonatti, Lorenzo J. Díaz  Mathematische Zeitschrift 176 (2014), pp. 469503.  /  
Universal regular control for generic semilinear systems  Nicolas Gourmelon  Mathematics of Control, Signals, and Systems 26 (2014), no. 4, pp. 481518.  /  
A geometric path from zero Lyapunov exponents to rotation cocycles  Andrés Navas  Ergodic Theory and Dynamical Systems 35 (2015), no. 2, pp. 374402.  /  
Perturbation of the Lyapunov spectra of periodic orbits  Christian Bonatti  Proceedings of the London Mathematical Society 105 (2012), no. 1, pp. 148.  /  
Nonuniform hyperbolicity, global dominated splittings and generic properties of volumepreserving diffeomorphisms  Artur Avila  Transactions of the American Mathematical Society 364 (2012), no. 6, pp. 28832907.  /  
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. 61106.  / Correction:  
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. 931979.  /  
Some characterizations of domination  Nicolas Gourmelon  Mathematische Zeitschrift 263 (2009), no. 1, pp. 221231.  /  
Uniformly hyperbolic finitevalued \({\rm SL}(2,\Bbb{R})\) cocycles  Artur Avila, JeanChristophe Yoccoz  Commentarii Mathematici Helvetici 85 (2010), no. 4, pp. 813884.  /  
\(C^1\)generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents    Journal of the Institute of Mathematics of Jussieu, 9 (2010), no. 1, pp. 4993.  /  
Cantor spectrum for Schrödinger operators with potentials arising from generalized skewshifts  Artur Avila, David Damanik  Duke Mathematical Journal 146 (2009), no. 2, pp. 253280.  /  
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), 407417.  /  
Generic expanding maps without absolutely continuous invariant \(\sigma\)finite measure  Artur Avila  Mathematical Research Letters 14 (2007), no. 5, 721730.  /  
A generic \(C^1\) map has no absolutely continuous invariant probability measure  Artur Avila  Nonlinearity 19 (2006), 27172725.  /  
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, 307349.  /  
A remark on conservative diffeomorphisms  Bassam Fayad, Enrique Pujals  Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), 763766.  /  
\(L^p\)generic cocycles have onepoint Lyapunov spectrum  Alexander Arbieto  Stochastics and Dynamics 3 (2003), 7381. Corrigendum. ibid, 3 (2003), 419420.  / +  
Lyapunov exponents: How frequently are dynamical systems hyperbolic?  Marcelo Viana  Modern dynamical systems and applications, 271297, Brin, Hasselblatt, Pesin (eds.) Cambridge Univ. Press, 2004.  Correction:  
Inequalities for numerical invariants of sets of matrices    Linear Algebra and its Applications, 368 (2003), 7181.  /  
The Lyapunov exponents of generic volume preserving and symplectic maps  Marcelo Viana  Annals of Mathematics, 161 (2005), no. 3, 14231485.  /  
Robust transitivity and topological mixing for \(C^1\)flows  Flavio Abdenur, Artur Avila  Proceedings of American Mathematical Society, 132 (2004), 699705.  /  
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), 113123.  /  
A formula with some applications to the theory of Lyapunov exponents  Artur Avila  Israel Journal of Mathematics, 131 (2002), 125137.  /  
Genericity of zero Lyapunov exponents    Ergodic Theory and Dynamical Systems, 22 (2002), 16671696.  / ,  
Discontinuity of the Lyapunov exponent for nonhyperbolic cocycles    Permanent preprint  , 
Last update: November, 2023. 