Session S03 - Geometric and Variational Methods in Celestial Mechanics

Wednesday, July 14, 16:30 ~ 17:10 UTC-3

On the global dynamics of the planar hyperbolic two-body problem

Mario Dias Carneiro

Federal University of Minas Gerais, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We discuss some results about the global dynamics of the hyperbolic two-body problem in the context of symplectic reduction and reconstruction of Hamiltonian with zero curvature principal bundle. We also show how the bifurcation of relative equilibria is an example of recent results by N. de Paula and P. Salomão [SP} about the global dynamics of Hamiltonians with a saddle-center singularity.

[SP] Pedro A. S. Salomão; DE PAULO, N. V. . Systems of transversal sections near-critical energy levels of Hamiltonian systems in R^4. Memoirs of the American Mathematical Society, v. 252, p. 1-105, 2018.

Joint work with Justino Muniz Jr ( Federal University of Viçosa) and Matthew Perlmutter (federal University of Minas Gerais-Brazil).

View abstract PDF