José Pedro Gaivão
Member of REM, CEMAPRE and of the Lisbon Dynamical Systems Group - LxDS.
Research interests:
Dynamical Systems, Hamiltonian dynamics, piecewise contractions, billiards and exponentially small phenomena.
Education:
Licenciatura in Matemática Aplicada à Tecnologia, Universidade do Porto, 2005.
PhD in Mathematics (supervisor: Vassili Gelfreich), University of Warwick, 2010.
Publications:
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Exponentially small splitting of invariant manifolds near a Hamiltonian-Hopf bifurcation
PhD thesis, University of Warwick, 2010.
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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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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.
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Analytic invariants for the 1:-1 resonance.
Annales de l'Institut Fourier, vol. 63, no.4, p. 1267-1426, 2013.
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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.
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Ergodicity of polygonal slap maps
(with G. Del Magno, J. L. Dias and P. Duarte)
Nonlinearity, 27, no.8, p. 1969-1983, 2014.
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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.
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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.
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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.
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$\lambda$-stability of periodic bililard orbits
(with S. Troubetzkoy)
Nonlinearity, 31, no.9, p. 4326, 2018.
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Linearization of Gevrey flows on $\mathbb{T}^d$ with a Brjuno type arithmetical condition
(with J. L. Dias)
Journal of Differential Equations, vol. 267, issue 12, p. 7167-7212, 2019.
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Asymptotic periodicity in outer billiards with contraction
Ergodic Theory and Dynamical Systems, vol. 40, issue 2, p. 402-417, 2020.
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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.
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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.
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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.
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Dynamics of piecewise increasing contractions
(with A. Nogueira)
Bulletin of the London Mathematical Society, Online First, doi: 10.1112/blms.12577, 2022.
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Billiards in generic convex bodies have positive topological entropy
(with M. Bessa, G. Del Magno, J. L. Dias, M. J. Torres)
Preprint, 2022.
Last update: 10 January 2022