Publications

João Lopes Dias

18 Articles in international journals with referee

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, 5359–5374 (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).


1 Books - author

Introdução à Integração em Rn
J. Lopes Dias
Coleção Económicas - 2.ª Série, Almedina, (2015).


5 Chapters in international books with referee

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).


4 Preprints

On the attractor of piecewise expanding maps of the interval
G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão
preprint (2018). PDF

Renormalization of Gevrey vector fields with a Brjuno type arithmetical condition
J. Lopes Dias and J. P. Gaivão
preprint (2017). PDF

Reducibility of quasi-periodically forced circle flows
S. Kocic and J. Lopes Dias
preprint (2016).

Ergodic properties of polygonal billiards with strongly contracting reflection laws
G. Del Magno, J. Lopes Dias, P. Duarte and J. P. Gaivão
preprint (2015).