Associate Professor
Associate Professor
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Research interests:
Dynamical Systems, Hamiltonian dynamics, piecewise dynamics and billiards.
Education:
PhD in Mathematics, University of Warwick, 2010
Exponentially small splitting of invariant manifolds near a Hamiltonian-Hopf bifurcation
Selected recent publications:
Multi-dimensional piecewise contractions are asymptotically periodic
(with B. Pires)
Ergodic Theory and Dynamical Systems, vol. 46, issue 4, p. 983-1008, 2026.Billiards in generic convex bodies have positive topological entropy
(with M. Bessa, G. Del Magno, J. L. Dias, M. J. Torres)
Advances in Mathematics, vol. 442, 109592, 2024.Dynamics of piecewise increasing contractions
(with A. Nogueira)
Bulletin of the London Mathematical Society, vol. 54, 482-500, 2022.
Preprints and working in progress:
Lyapunov exponents and rigidity in random billiards and standard maps
(with G. Del Magno and J. L. Dias)
arXiv preprint, 2026.Brjuno condition through best approximations and the linearization problem
(with N. Chevallier, J. L. Dias, A. Marnat and N. Moshchevitin)Generic properties of planar symplectic billiards
(with L. Baracco and O. Bernardi)Rigidity in random symplectic diffeomorphisms of T^2
(with G. Del Magno and J. L. Dias)Partial best-response dynamics in anti-coordination games
(with T. Peixe)
Publications:
Multidimensional contracted rotations
(with B. Pires)
Proceedings of the American Mathematical Society, to appear, 2026.Multi-dimensional piecewise contractions are asymptotically periodic
(with B. Pires)
Ergodic Theory and Dynamical Systems, vol. 46, issue 4, p. 983-1008, 2026.Hausdorff dimension of the exceptional set of interval piecewise affine contractions
Qualitative Theory of Dynamical Systems, vol. 24, 86, 2025.Rotation number of 2-interval piecewise affine maps
(with M. Laurent and A. Nogueira)
Aequationes Mathematicae, 99, 511–530, 2025.Billiards in generic convex bodies have positive topological entropy
(with M. Bessa, G. Del Magno, J. L. Dias, M. J. Torres)
Advances in Mathematics, vol. 442, 109592, 2024.Dynamics of piecewise increasing contractions
(with A. Nogueira)
Bulletin of the London Mathematical Society, vol. 54, 482-500, 2022.Hyperbolic polygonal billiards close to 1-dimensional piecewise expanding maps
(with G. Del Magno, J. L. Dias, P. Duarte)
Journal of Statistical Physics, vol. 182, No. 11, 2021.Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game
(with T. Peixe)
Dynamic Games and Applications,11(3), 491-511, 2021.On the attractor of piecewise expanding maps of the interval
(with G. Del Magno, J. L. Dias, P. Duarte)
Stochastics and Dynamics, vol. 20, No. 02, 2050009, 2020.Asymptotic periodicity in outer billiards with contraction
Ergodic Theory and Dynamical Systems, vol. 40, issue 2, p. 402-417, 2020.Linearization of Gevrey flows on 𝕋d with a Brjuno type arithmetical condition
(with J. L. Dias)
Journal of Differential Equations, vol. 267, issue 12, p. 7167-7212, 2019.λ-stability of periodic bililard orbits
(with S. Troubetzkoy)
Nonlinearity, 31, no.9, p. 4326, 2018.Hyperbolic polygonal billiards with finitely many ergodic SRB measures
(with G. Del Magno, J. L. Dias, P. Duarte)
Ergodic Theory and Dynamical Systems, vol. 38, issue 6, p. 2062-2085, 2018.Hyperbolic billiards on polytopes with contracting reflection laws
(with P. Duarte and M. Soufi)
Discrete and Continuous Dynamical Systems - Series A, vol. 37, no. 6, p. 3079-3109, 2017.Dissipative outer billiards: a case study
(with G. Del Magno and E. Gutkin)
Dynamical Systems: An International Journal, vol. 30, no.1, p. 45-69, 2015.Ergodicity of polygonal slap maps
(with G. Del Magno, J. L. Dias and P. Duarte)
Nonlinearity, 27, no.8, p. 1969-1983, 2014.SRB measures for polygonal billiards with contracting reflection laws
(with G. Del Magno, J. L. Dias, P. Duarte and D. Pinheiro)
Communications in Mathematical Physics, vol. 329, 2, p. 687-723, 2014.Analytic invariants for the 1:-1 resonance.
Annales de l'Institut Fourier, vol. 63, no.4, p. 1267-1426, 2013.Chaos in the square billiard with a modified reflection law
(with G. Del Magno, J. L. Dias, P. Duarte and D. Pinheiro)
Chaos, 22, 026106, 2012.Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift-Hohenberg equation as an example
(with V. Gelfreich)
Nonlinearity, 24, no.3, p. 677-698, 2011.
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