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Permanent Faculty

Name: Rafael Ruggiero
Title: PhD, IMPA 1989
Office: 863L
Position: Associate Professor
Phone: 3527-1743
E-mail: rorr
Research Areas: Dynamical Systems

I have been interested in the last 3 years on generic theory for Hamiltonians from Mañé's viewpoint, as well as on rigidity problems concerning Finsler geometry and weakly integrable Hamiltonian systems.A sample of some recent results: with Professor Ludovic Rifford of the University of Nice, Sophia-Antipolis, we show that generic properties of closed orbits of Hamiltonians in a fixed energy level are also generic from Mañé's viewpoint, namely, Hamiltonian genericity in this case is attained by perturbations by potentials or just by perturbations involving horizontal variables of the cotangent bundle (see ref. 1). This result improves Takens, Takens-Klingenberg results in the 1970's, and simplifies a great deal their proofs by the use of control theory. In what concerns Finsler geometry and integrable systems, we show with Professor José Barbosa Gomes of the UFJF that Finsler compact surfaces of genus greater than 1 without conjugate points have an invariant, codimension 1 foliation conjugated to a hyperbolic central foliation. Applying this result we get that Finsler-Landsberg metrics on such surfaces are actually Riemannian (see ref. n. 2). In another paper with the same co-author, we show that k-basic Finsler metrics without conjugate points on tori where Busemann's foliations are differentiable with Lipschitz first derivatives have zero flag curvature, a partial version of the Hopf conjecture for k-basic Finsler metrics (see ref. N. 3). In a recente paper, we show the Hopf conjecture for k-basic Finsler metrics on tori ithout conjugate points which are analytic.

 Lattes CV   |  Research Results

  Mathematics Department / PUC-Rio
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