# 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]
*“On the dynamics of minimal homeomorphisms of* **T**²* which are not pseudo-rotations*” (2016) [ArXiv]

## Publications

*“Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms” *Accepted in **Mathematische Zeitschrift **(2017). Joint with Fernanda Pereira Rodrigues [ArXiv]
*“Structural stability of the inverse limit of endomorphisms”. ***Annales de l’Institut Henri Poincaré – Analyse Non Linéaire** (2017), 34, 1227-1253. Joint with Pierre Berger [Journal] [ArXiv]
*“On first integrals of the geodesic flow on Heisenberg nilmanifolds”. ***Differential Geometry and its Applications** (2016), 49, 496–509. Joint with Gabriela Ovando and Silvio Reggiani [Journal] [ArXiv]
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*Livsic theorem for low-dimensional diffeomorphism cocycles*“. **Commentarii Mathematici Helvetici** (2016), 91, 39-64. Joint with Rafael Potrie [Journal] [ArXiv]
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*Cohomology of dominated diffeomorphism-valued cocycles over hyperbolic systems*“. **Ergodic Theory & Dynamical Systems** (2016), 36, 1703-1722. Joint with Lucas Backes [Journal] [ArXiv]
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*On manifolds supporting distributionally uniquely ergodic diffeomorphisms*“. **Journal of Differential Geometry** (2015), 99, 191-213. Joint with Artur Avila and Bassam Fayad [Journal] [ArXiv]
*“On cohomological C⁰-(in)stability”. ***Bulletin of the Brazilian Mathematical Society** (2013), 44, pp. 489-495 [Journal] [ArXiv]
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*Cohomological equations and invariant distributions for minimal circle diffeomorphisms*“. **Duke Mathematical Journal** (2011), 158, pp. 501-536. Joint with Artur Avila [Journal] [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]