Research

"Sim, sei bem //Que nunca serei alguém.// Sei de sobra// Que nunca terei uma obra.
Sei, enfim,//Que nunca saberei de mim.//Sim, mas agora,//Enquanto dura esta hora,
Este luar, estes ramos,//Esta paz em que estamos,//Deixem me crer//O que nunca poderei ser."
Fernando Pessoa, Odes a Ricardo Reis.

My research interests lie in the areas of dynamical systems and ergodic theory. More precisely, my main works have focused on cohomology and Lyapunov exponents of cocycles over hyperbolic systems. More recently, I have been also interested in problems involving the shadowing property and linearization of nonautonomous systems.

Papers

You can find below a list with my recent papers and preprints. Full texts can be accessed by clicking either on the respective titles (for arxiv versions) or on the journal's name (this may require that you have access to the journal's content).

• Rigidity of fiber bunched cocycles

Bulletin of the Brazilian Mathematical Society, Volume 46, Issue 2, pp 163–179, June 2015.

• Cohomology of dominated diffeomorphism-valued cocycles over hyperbolic systems

Joint with Alejandro Kocsard. Ergodic Theory & Dynamical Systems, Volume 36, Issue 6, pp 1703-1722, September 2016.

• On the periodic approximation of Lyapunov exponents for semi-invertible cocycles

Discrete and Continuous Dynamical Systems - Series A, Volume 37, Issue 12, pp 6353–6368, December 2017.

• Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces

Joint with Mauricio Poletti. Stochastics and Dynamics, Volume 17, Number 06, 1750047, December 2017.

• Continuity of Lyapunov exponents for cocycles with invariant holonomies

Joint with Aaron Brown and Clark Butler. Journal of Modern Dynamics, Volume 12, pp 223–260, 2018.

• Periodic approximation of Oseledets subspaces for semi-invertible cocycles

Dynamical Systems: an International Journal, Volume 33, Issue 3, pp 480–496, 2018.

• The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open

Joint with Mauricio Poletti and Adriana Sánchez. Mathematical Research Letters, Volume 25, Number 6, pp 1719–1740, 2018.

• Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles

Joint with Davor Dragičević. Annales Academiae Scientiarum Fennicae, Volume 44, pp 183–209, 2019.

• Shadowing for nonautonomous dynamics

Joint with Davor Dragičević. Advanced Nonlinear Studies, Volume 19, Issue 2, pp 425–436, 2019.

• A remark on the invertibility of semi-invertible cocycles

Journal of Dynamical and Control Systems, Volume 25, Issue 4, pp 527–533, 2019.

• A Livšic theorem for matrix cocycles over non-uniformly hyperbolic systems

Joint with Mauricio Poletti. Journal of Dynamics and Differential Equations, Volume 31, Issue 4, pp 1825–1838, 2019.

• Quasi-shadowing for partially hyperbolic dynamics on Banach spaces

Joint with Davor Dragičević. Journal of Mathematical Analysis and Applications, Volume 492, Issue 1, pp 124445, 2020.

• Cohomology of fiber-bunched twisted cocycles over hyperbolic systems

Proceedings of the Edinburgh Mathematical Society, Volume 63, Issue 3, pp 844-860, 2020.

• Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems

Joint with Mauricio Poletti, Paulo Varandas and Yuri Lima. Ergodic Theory & Dynamical Systems, Volume 40, Issue 11, pp 2947-2969, 2020.

• Shadowing for infinite dimensional dynamics and exponential trichotomies

Joint with Davor Dragičević. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 151 , Issue 3 , pp 863-884, 2021.

• Hyers-Ulam stability for hyperbolic random dynamics

Joint with Davor Dragičević. Fundamenta Mathematicae, Volume 255, pp 69-90, 2021.

• A Rolewicz-type characterization of nonuniform behaviour

Joint with Davor Dragičević. Applicable Analysis, Volume 100, Issue 14, pp 3011-3032, 2021.

• On the spectral radius of compact operator cocycles

Joint with Davor Dragičević. Stochastics and Dynamics, Volume 21, Number 05, 2150026, 2021.

• A general approach to nonautonomous shadowing for nonlinear dynamics

Joint with Davor Dragičević. Bulletin des Sciences Mathématiques, Volume 170, Article 102996 (30 pp), 2021.

• Linearization and Hölder Continuity for Nonautonomous Systems

Joint with Davor Dragičević and Kenneth J. Palmer. Journal of Differential Equations, Volume 297, pp 536-574, 2021.

• Shadowing for nonautonomous and nonlinear dynamics with impulses

Joint with Davor Dragičević and Lokesh Singh. Monatshefte für Mathematik, Volume 198, Issue 3, pp 485-502, 2022.

• A generalized Grobman-Hartman theorem for nonautonomous dynamics

Joint with Davor Dragičević. Collectanea Mathematica, Volume 73, Issue 3, pp 411-431, 2022.

• Topological pressure for discontinuous semiflows and a variational principle for impulsive dynamical systems

Joint with Fagner Rodrigues. Topological Methods in Nonlinear Analysis, Volume 59, Issue 1, pp 303-330, 2022.

• Weighted shadowing for delay differential equations

Joint with Davor Dragičević, Mihály Pituk and Lokesh Singh. Archiv der Mathematik, Volume 119, Issue 5, pp 539-552, 2022.

• On the linearization of infinite-dimensional random dynamical systems

Joint with Davor Dragičević. Mathematische Nachrichten, Volume 296, Issue 8, pp 3173-3191, 2023.

• Multiscale linearization of nonautonomous systems

Joint with Davor Dragičević. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 153, Issue 5, pp. 1609-1629, 2023.

• A variational principle for the metric mean dimension of level sets

Joint with Fagner Rodrigues. IEEE Transactions on Information Theory, Volume 69, Issue 9, pp. 5485-5496, 2023.

• Smooth linearization of nonautonomous coupled systems

Joint with Davor Dragičević. Discrete and Continuous Dynamical Systems - Series B, Volume 28, Issue 8, pp 4497-4518, 2023.

• Parameterized shadowing for nonautonomous dynamics

Joint with Davor Dragičević and Xiao Tang. Journal of Mathematical Analysis and Applications, Volume 529, Issue 1, pp 127584, 2024.

• Conditional Lipschitz shadowing for ordinary differential equations

Joint with Davor Dragičević, Masakazu Onitsuka and Mihály Pituk. To appear in Journal of Dynamics and Differential Equations.

• Smooth linearization of nonautonomous dynamics under polynomial behaviour

Joint with Davor Dragičević and Wenmeng Zhang. Preprint.

• Shadowing, Hyers-Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

Joint with Davor Dragičević and Mihály Pituk. To appear in Communications in Contemporary Mathematics.

Book

Uma introdução aos sistemas dinâmicos via exemplos Joint with Alexandre T. Baraviera and Flávia M. Branco. Published by IMPA for the 34th Brazilian Mathematics Colloquium, 2023.