December  2008, 1(4): 611-629. doi: 10.3934/dcdss.2008.1.611

The 2-body problem under Fock's potential

1. 

Astronomical Institute of the Romanian Academy, Str. Cutitul de Argint 5, RO-75212 Bucharest, Romania

2. 

Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340, Mexico

Received  April 2008 Revised  July 2008 Published  September 2008

We study the two-body problem moving under the Fock's potential, where the global flow is fully described. The analysis is separately performed for negative, zero, and positive energy levels. Many kinds of orbits are found, some of them being of positive Lebesgue measure. We also show some unusual features as the coexistence of fundamentally different orbits for the same energy level and for the same angular momentum.
Citation: Vasile Mioc, Ernesto Pérez-Chavela. The 2-body problem under Fock's potential. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 611-629. doi: 10.3934/dcdss.2008.1.611
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