Integrantes: J. Vieitez, A. Artigue, M. Achigar.
Temas de investigación en Sistemas Dinámicos:
- Dinámica topológica: Sistemas expansivos, Nociones de recurrencia, Funciones de Lyapunov, estabilidad, atractores y repulsores, Entropía topológica, Teoría de continuos en dinámica.
- Teoría general de sistemas diferenciables: Conjuntos hiperbólicos, Hiperbolicidad parcial y descomposición dominada, Sistemas de origen geométrico, Dinámicas con singularidades y billares.
- Sistemas dinámicos en dimensiones pequeñas: Mapas del intervalo y del círculo, Homeomorfismos y difeomorfismos del plano y de superficies, Flujos en superficies.
- Aplicaciones a las ciencias naturales: Sistemas dinámicos en física y biología, Análisis numérico de sistemas dinámicos.
Publicaciones:
A. Artigue, Meihua Dong, Lipschitz Structural Stability of Group Actions with the Shadowing Property, J. Differential Equations, Vol. 366 (2023).
A. Arbieto, A. Artigue, E. Rego, Rescaled-Expansive Flows: Unstable Sets and Topological Entropy, prepublicación 2021.
A. Artigue, B. Carvalho, W. Cordeiro, J. Vieitez, Continuum-wise hyperbolicity, Journal of Differential Equations, Vol 378, p. 512-538, (2024).
M. Achigar, Extensions of expansive dynamical systems, por aparecer en Discrete and Continuous Dynamical Systems.
E. Akin, A. Artigue, L. Ferrari, Asymptotic Pairs for Interval Exchange Transformations.
2022
A. Artigue, B. Carvalho, W. Cordeiro, J. Vieitez, Countably and entropy expansive homeomorphisms with the shadowing property, Proceedings of the AMS, Vol. 150, (2022).
A. Artigue, On continuum-wise minimality, Fundamenta Mathematicae, Vol. 258, (2022).
A. Artigue, W. Cordeiro, M.J. Pacifico, N-expansive flows, Topology and its Applications, Vol. 305, (2022).
2021
M. Achigar, Expansive systems on lattices, Topology and its Applications, Vol. 290, (2021).
2020
M. Achigar, A. Artigue, J. Vieitez. New cw-expansive homeomorphisms of surfaces, Annales Mathématiques Toulouse, Tome XXIX, (2020), p. 221-246.
M.J. Pacifico y J.L. Vieitez, Lyapunov exponents for expansive homeomorphisms, Proceedings of the Edinburgh Mathematical Society, Vol. 63, 2020, pp. 413-425.
A. Artigue, Local stable sets of almost periodic points, Topology and its Applications, Vol. 272, (2020).
A. Artigue, B. Carvalho, W. Cordeiro, J. Vieitez, Beyond topological hyperbolicity: the L-shadowing property, Journal of Differential Equations, Vol. 268, 2020, pp. 3057-3080.
A. Artigue, M. Haim, Expansivity on Commutative Rings, Topology and its Applications, Vol. 274, (2020).
2019
M. Achigar, A Note on Anosov Homeomorphisms, Special Issue «Shadowing in Dynamical Systems» Axioms, Ed. K. Sakai, Vol. 8, 2019.
A. Artigue, G. Cousillas, Generic homeomorphisms with shadowing of one-dimensional continua, Special Issue «Shadowing in Dynamical Systems» Axioms, Ed. K. Sakai, Vol. 8, 2019.
A. Artigue, Billiards and toy gravitons, Journal of Statistical Physics, Vol. 175, 2019, pp 213-232.
A. Artigue, Generic dynamics on compact metric spaces, Topology and its Applications, Vol. 255, 2019, pp. 1-14.
A. Artigue, An expansive homeomorphism of a 3-manifold with a local stable set that is not locally connected, Fundamenta Mathematicae, Vol. 245, 2019, pp. 167-174.
2018
M. Achigar, A. Artigue, I. Monteverde, Observing expansive maps, Journal of the London Mathematical Society, Vol. 98, 2018, pp. 501-516.
A. Artigue, Rescaled expansivity and separating flows, Discrete and Continuous Dynamical Systems, Vol. 38, pp. 4433-4447, 2018.
A. Artigue, Dendritations of surfaces, Ergodic Theory and Dynamical Systems, Vol. 38, pp 2860-2912, 2018.
A. Artigue, Self-similar hyperbolicity, Ergodic Theory and Dynamical Systems, Vol. 38, pp. 2422-2446, 2018.
2017
A. Artigue, D. Carrasco, I. Monteverde, Polynomial entropy and expansivity, Acta Mathematica Hungarica, Volume 152, Issue 1, pp 140–149, 2017.
A. Artigue, M.J. Pacifico, J.L. Vieitez, N-expansive homeomorphisms on surfaces, Communications in Contemporary Mathematics, Vol. 19, 2017.
A. Artigue, Pseudo-Anosov maps and continuum theory, Proceedings of the American Mathematical Society, Vol. 145, 2017, pp. 3047-3056.
A. Artigue, Singular cw-expansive flows, Discrete and Continuous Dynamical Systems, Vol. 37, 2017, pp. 2945-2956.
A. Artigue, Separating homeomorphisms, Advances in Dynamical Systems and Applications, Vol. 12, 2017, pp. 17-24.
A. Artigue, Isolated sets, catenary Lyapunov functions and expansive systems, Topological Methods in Nonlinear Analysis, Vol. 49, 2017, pp. 21-50.
C. Bonatti, I. Monteverde, A. Navas, C. Rivas, Rigidity for C1 actions on the interval arising from hyperbolicity I: solvable groups, Mathematische Zeitschrift, 2017.
2016
M. Achigar, A. Artigue, I. Monteverde, Expansive homeomorphisms on non-Hausdorff spaces, Topology and its Applications, 2016.
A. Artigue, Kinematic expansive flows, Ergodic Theory and Dynamical Systems, Vol. 36, 2016, pp. 390–421.
A. Artigue, Robustly N-expansive surface diffeomorphisms, Discrete and Continuous Dynamical Systems, Vol. 36, 2016, pp. 2367–2376.
A. Artigue, Anomalous cw-expansive surface homeomorphisms, Discrete and Continuous Dynamical Systems, Vol. 36, 2016, pp. 3511–3518.
A. Artigue, Discrete and continuous topological dynamics: Fields of cross sections and expansive flows, Discrete and Continuous Dynamical Systems, Vol. 36, 2016, pp. 5911-5927.
2015
A. Artigue, Finite sets with fake observable cardinality, Bulletin of the Korean Mathematical Society, Vol. 52, 2015, pp. 323–333.
A. Artigue, Minimal expansive systems and spiral points, Topology and its Applications, Vol. 194, 2015, pp. 166–170.
A. Artigue, Lipschitz perturbations of expansive systems, Discrete and Continuous Dynamical Systems, Vol. 35, 2015, pp. 1829–1841.
A. Artigue, Expansive flows of the three-sphere, Differential Geometry and its Applications, Vol. 41, 2015, pp. 91–101.
A. Artigue, D. Carrasco, A note on measure-expansive diffeomorphisms, Journal of Mathematical Analisys and Applications, Vol. 428, 2015, pp. 713–716.
M.J. Pacifico, J.L. Vieitez, On measure expansive diffeomorphisms, Proc. Amer. Math. Soc. 143 (2015), no. 2, 811–819.
2014
A. Artigue, Low-Dimensional Homoclinic Bifurcations of Repellers, Int. J. of Bifurcation and Chaos, Vol. 24, 2014
A. Artigue, Positive expansive flows, Topology and its Applications, Vol. 165, pp. 121–132, 2014.
J. Groisman, J.L. Vieitez, On transitive expansive homeomorphisms of the plane, Topology and its Applications, 2014.
2013
A. Artigue, Expansive flows of surfaces, Discrete and Continuous Dynamical Systems, Vol. 33, 2013, pp. 505–525.
A. Artigue, Hyper-expansive homeomorphisms, Publicaciones Matemáticas del Uruguay, Vol. 14, 2013, pp. 72–77.
R. Markarian, M.J. Pacifico, J.L. Vieitez, Exponential speed of mixing for skew-products with singularities, Nonlinearity 26 (2013), 269–287
R. Markarian, M.J. Pacifico, J.L. Vieitez, Corrigendum: Exponential speed of mixing for skew-products with singularities, Nonlinearity 26 (2013), 2923
2012
L.J. Díaz, T. Fisher, M.J. Pacifico, J.L. Vieitez, Entropy-expansiveness for partially hyperbolic diffeomorphisms, Discrete Contin. Dyn. Syst. 32 (2012), 4195–4207
J.J. Nieto, M.J. Pacifico, J.L. Vieitez, Long-term and short-term dynamics of Microtus epiroticus: a Yoccoz-Birkeland model, SIAM J. Appl. Dyn. Syst. 11 (2012), 1499–1532