Billiards in generic convex bodies have positive topological entropy
M. Bessa, G. Del Magno, J. Lopes Dias, J. P. Gaivão and M. J. Torres
Advances in Mathematics 441, 109592 (2024).
Dynamics of piecewise increasing contractions
J. P. Gaivão and A. Nogueira
Bulletin of the London Mathematical Society, to appear (2021).
Hyperbolic polygonal billiards close to 1-dimensional piecewise expanding maps
G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão
Journal of Statistical Physics 182, 11 (2021).
Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game
J. P. Gaivão and T. Peixe
Dynamic Games and Applications 11 (3), 491-511 (2021).
Asymptotic periodicity in outer billiards with contraction
J. P. Gaivão
Ergodic Theory and Dynamical Systems 40, 402-417 (2020).
The attractor of piecewise expanding maps of the interval
G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão
Stochastics and Dynamics 20, 2050009 (2020).
Linearization of Gevrey flows on $\mathbb{T}^d$ with a Brjuno type arithmetical condition,
J. Lopes Dias and J. P. Gaivão
Journal of Differential Equations 267, 7167-7212 (2019).
$\lambda$-stability of periodic billiard orbits
J. P. Gaivão and S. Troubetzkoy
Nonlinearity 31(9), 4326 (2018).
Hyperbolic polygonal billiards with finitely many ergodic SRB measures
G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão
Ergodic Theory and Dynamical Systems 38, 2062-2085 (2018).
Hyperbolic billiards on polytopes with contracting reflection laws
P. Duarte, J. P. Gaivão and M. Soufi
Discrete and Continuous Dynamical Systems - A 37(6), 3079-3109 (2017).
Dissipative outer billiards: a case study
G. Del Magno, J. P. Gaivão and E. Gutkin
Dynamical Systems 30, 45-69 (2015).
Ergodicity of polygonal slap maps
G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão
Nonlinearity 27, 1969-1983 (2014).
SRB measures for polygonal billiards with contracting reflection laws
G. Del Magno, J. Lopes Dias, P. Duarte, J. P. Gaivão and D. Pinheiro
Communications in Mathematical Physics 329, 687-723 (2014).
Analytic invariants for the 1:-1 resonance
J. P. Gaivão
Annales de l'Institut Fourier 63, 1367-1426 (2013).
Chaos in the square billiard with a modified reflection law
G. Del Magno, J. Lopes Dias, P. Duarte, J. P. Gaivão and D. Pinheiro
Chaos 22, 026106 (2012).
Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the SwiftHohenberg equation as an example
J. P. Gaivão and V. Gelfreich
Nonlinearity 24, 677-698 (2011).
New Trends in Lyapunov Exponents, NTLE, Lisbon, Portugal, February 7–11, 2022
J. Lopes Dias, P. Duarte, J. P. Gaivão, S. Klein, T. Peixe, J. Siqueira and M. J. Torres
CIM Series in Mathematical Sciences, Springer VII, (2023).
Polygonal billiards with a contractive reflection law: a review of some hyperbolic properties
G. Del Magno, J. Lopes Dias, P. Duarte, J. P. Gaivão and D. Pinheiro
in Difference Equations, Discrete Dynamical Systems and Applications, Eds. L. Alseda i Soler et al., Springer 180, (2016).
Hausdorff dimension of the exceptional set of interval piecewise affine contractions
J. P. Gaivão
preprint (2022).
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Rotation number of 2-interval piecewise affine maps
J. P. Gaivão, M. Laurent and A. Nogueira
preprint (2022).
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