# Research

## Areas of interest

I am mainly interested on low-dimensional dynamics, cohomological aspects of dynamical systems, (partially) hyperbolic dynamics and small denominators phenomena (KAM theory)

## Preprints

• “Livsic theorem for diffeomorphism cocycles” (2017). Joint with Artur Avila and Xiao-Chuan Liu [ArXiv]
• “Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms” (2017). Joint with
• “On the dynamics of minimal homeomorphisms of T2 which are not pseudo-rotations” (2016) [ArXiv]

## Publications

• “Structural stability of the inverse limit of endomorphisms”. Accepted in Annales de l’Institut Henri Poincaré – Analyse Non Linéaire (2015). Joint with
• “On first integrals of the geodesic flow on Heisenberg nilmanifolds”. Differential Geometry and its Applications (2016), 49, 496–509. Joint with Gabriela Ovando and [ArXiv]
• Livsic theorem for low-dimensional diffeomorphism cocycles“. Commentarii Mathematici Helvetici (2016), 91, 39-64. Joint with [ArXiv]
• Cohomology of dominated diffeomorphism-valued cocycles over hyperbolic systems“. Ergodic Theory & Dynamical Systems (2016), 36, 1703-1722. Joint with [ArXiv]
• On manifolds supporting distributionally uniquely ergodic diffeomorphisms“. Journal of Differential Geometry (2015), 99, 191-213. Joint with Artur Avila and [ArXiv]
• “On cohomological C0-(in)stability”. Bulletin of the Brazilian Mathematical Society (2013), 44, pp. 489-495 [Journal] [ArXiv]
• Cohomological equations and invariant distributions for minimal circle diffeomorphisms“. Duke Mathematical Journal (2011), 158, pp. 501-536. Joint with [ArXiv]
• “Cohomologically rigid vector fields: the Katok conjecture in dimension 3”. Annales de l’Institut Henri Poincaré – Analyse Non Linéaire (2009), 26, pp. 1165-1182 [Journal] [ArXiv]
• “A mixing-like property and inexistence of invariant foliations for minimal diffeomorphisms of the 2-torus”. Proceedings of the American Mathematical Society (2009), 137, pp. 3379-3386. Joint with Andrés Koropecki [Journal] [ArXiv]
• “Free curves and periodic points for torus homemorphisms”. Ergodic Theory & Dynamical Systems (2008), 28, pp. 1895-1915. Joint with Andrés Koropecki [Journal] [ArXiv]