João Lopes Dias

Expansiveness and hyperbolicity in convex billiards

M. Bessa, J. Lopes Dias and M. J. Torres

*Regular & Chaotic Dynamics* 26, 756-762 (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).

Hyperbolicity through stable shadowing for generic geodesic flows

M. Bessa, J. Lopes Dias and M. J. Torres

*Physica D: Nonlinear Phenomena* 406, 132423 (2020).

Reducibility of quasi-periodically forced circle flows

S. Kocic and J. Lopes Dias

*Discrete and Continuous Dynamical Systems - A* 40, 5325-5345 (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).

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).

On shadowing and hyperbolicity for geodesic flows on surfaces

M. Bessa, J. Lopes Dias and M. J. Torres

*Nonlinear Analysis: Theory, Methods & Applications* 155, 250-263 (2017).

Ergodicity of polygonal slap maps

G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão

*Nonlinearity* 27, 1969-1983 (2014).

Hamiltonian suspension of perturbed Poincaré sections and an application

M. Bessa and J. Lopes Dias

*Mathematical Proceedings of the Cambridge Philosophical Society* 157, 101-112 (2014).

Realization of tangent perturbations in discrete and continuous time conservative systems

H. N. Alishah and J. Lopes Dias

*Discrete and Continuous Dynamical Systems - A* 34, 53595374 (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).

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).

On the Herman-Avila-Bochi formula for Lyapunov exponents of $SL(2,\mathbb R)$-cocycles

A. T. Baraviera, J. Lopes Dias and P. Duarte

*Nonlinearity* 24, 2465-2476 (2011).

Hamiltonian elliptic dynamics on symplectic 4-manifolds

M. Bessa and J. Lopes Dias

*Proceedings of the American Mathematical Society* 137, 585-592 (2009).

Generic dynamics of 4-dimensional $C^2$ Hamiltonian systems

M. Bessa and J. Lopes Dias

*Communications in Mathematical Physics* 281, 597-619 (2008).

Local conjugacy classes for analytic torus flows

J. Lopes Dias

*Journal of Differential Equations* 245, 468-489 (2008).

Renormalization of diophantine skew flows, with applications to the reducibility problem

H. Koch and J. Lopes Dias

*Discrete and Continuous Dynamical Systems - A* 21, 477-500 (2008).

Multidimensional continued fractions, dynamic renormalization and KAM theory

K. Khanin, J. Lopes Dias and J. Marklof

*Communications in Mathematical Physics* 270, 197-231 (2007).

A normal form theorem for Brjuno skew-systems through renormalization

J. Lopes Dias

*Journal of Differential Equations* 230, 1-23 (2006).

Brjuno condition and renormalization for Poincaré flows

J. Lopes Dias

*Discrete and Continuous Dynamical Systems - A* 15, 641-656 (2006).

Renormalization for multidimensional Hamiltonian flows

K. Khanin, J. Lopes Dias and J. Marklof

*Nonlinearity* 19, 2727-2753 (2006).

Renormalization of flows on the multidimensional torus close to a $KT$ frequency vector

J. Lopes Dias

*Nonlinearity* 15, 647-664 (2002).

Renormalization scheme for vector fields on $\mathbb{T}^2$ with a diophantine frequency

J. Lopes Dias

*Nonlinearity* 15, 665-679 (2002).

Introdução à Integração em $\mathbb{R}^n$

J. Lopes Dias

*Coleção Económicas - 2.ª Série*, Almedina, (2015).

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).

From ice to penguins: the role of mathematics in Antarctic research

J. C. Xavier, S. L. Hill, M. Belchier, T. Bracegirdle, E. J. Murphy and J. Lopes Dias

*in Mathematics of Planet Earth. CIM Series in Mathematical Sciences, Eds. Bourguignon, Jeltsch, Pinto and Viana*, Springer, (2014).

Review on non-perturbative reducibility of quasi-periodically forced linear flows with two frequencies

J. Lopes Dias

*in Dynamics, Games and Science. CIM Series in Mathematical Sciences, Eds. Bourguignon, Jeltsch, Pinto and Viana*, Springer, 253-271 (2014).

Generic Hamiltonian dynamical systems: an overview

M. Bessa and J. Lopes Dias

*Dynamics, Games and Science I, Eds. Peixoto, Pinto and Rand*, Springer, 123-138 (2011).

KAM theory as a limit of renormalization

J. Lopes Dias

*Dynamics, Games and Science I, Eds. Peixoto, Pinto and Rand*, Springer, 253-270 (2011).

Billiards in generic convex bodies have positive topological entropy

M. Bessa, G. Del Magno, J. Lopes Dias, J. P. Gaivão and M. J. Torres

* preprint* (2022).
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