The 2-body problem under Fock's potential

Vasile Mioc; Ernesto Pérez-Chavela

doi:10.3934/dcdss.2008.1.611

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2008, Volume 1, Issue 4: 611-629. Doi: 10.3934/dcdss.2008.1.611

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The 2-body problem under Fock's potential

Vasile Mioc^1, and
Ernesto Pérez-Chavela^2,

1.
Astronomical Institute of the Romanian Academy, Str. Cutitul de Argint 5, RO-75212 Bucharest
2.
Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340

Received: March 31, 2008

Revised: June 30, 2008

Published: November 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 70F05, 70F16; Secondary: 34C05.

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