Permanent Faculty: Rafael O. Ruggiero

Rafael O. Ruggiero

PhD, IMPA, 1989
Office: 869
Position: Associate Professor
Phone: (21) 3527-1743
E-mail: rorr
Geometry, Dynamical Systems, Topology

Lattes CV

Professor Rafael Oswaldo Ruggiero obtained his PhD in pure Mathematics at IMPA ,Rio de Janeiro Brazil, in 1980 under the tutoring of Ricardo Mañé Ramirez. He is Professor of the Mathematics Department of PUC-Rio since 1989. His main research fields are dynamical systems from geometric origin, Lagrangian and Hamiltonian mechanics, Differential Geometry and topology.

He has been visiting professor at the École Normale de Lyon from 1993 to 1994, at the École Normale de Paris from september 2008 to march 2009, at the Université de Nice, Sophia-Antipolis in January-February 2014, and at the Université de Aix-Marseille and Université du Vaucluse, Avignon, from January to july 2017, among many other institutions during shorter periods.

Research Results

The research work of Professor Ruggiero during the last 5 years focused on rigidity problems in Finsler geometry, geometric control theory applied to the study of generic properties of Hamiltonian dynamics, ergodic theory of nonuniformly hyperbolic geodesic flows, and Lagrangian singularity theory combined with Aubry-Mather theory applied to the study of Birkhoff problems for Lagrangian invariant manifolds. He is member of many research groups in Brazil and France: Hamltonian dynamics with Professor Mário J. Carneiro from UFMG, thermodynamics formalism with Professor Artur Lopes from UFRGS, geodesic flows of Riemannian and Finsler metrics with Professors J. Barbosa from UFJF, Patrick Foulon from CIRM, Marseille, Katrin Gelfert from UFRJ, and Gérard Besson from Université de Grenoble, and geometric control theory with Professor Ludovic Rifford from Nice University.

The most recent publications of Professor Ruggiero are:

1) Geodesic flows modeled by expansive flows. With Katrin Gelfert, Proceedings of the Edinburgh Mathematical Society, 2019, vol. 62 (1) 61-95.

2) On the graph theorem for Lagrangian minimizing tori. With Mário Jorge Carneiro, Discrete and Continuous Dynamical systems,vol. 38 (12) 6029-6045.

3) On the C1,b denstiy of metrics without invariant graphs. With Rodrigo Pacheco, Discrete and Continuous Dymaical systems vol. 38 (1) 247-261.