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Scattering invariants in Euler's two-center problem
- Source :
- Nonlinearity, 32(4), 1296-1326. IOP PUBLISHING LTD
- Publication Year :
- 2018
- Publisher :
- arXiv, 2018.
-
Abstract
- The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an important role both in celestial mechanics and in the microscopic world. In the present paper we study the spatial problem in the case of arbitrary (both positive and negative) strengths of the centers. Combining techniques from scattering theory and Liouville integrability, we show that this spatial problem has topologically non-trivial scattering dynamics, which we identify as scattering monodromy. The approach that we introduce in this paper applies more generally to scattering systems that are integrable in the Liouville sense.
- Subjects :
- Integrable system
General Physics and Astronomy
FOS: Physical sciences
01 natural sciences
CLASSIFICATION
Hamiltonian system
Action-angle coordinates
INTEGRABLE HAMILTONIAN-SYSTEMS
symbols.namesake
scattering map
0101 mathematics
MONODROMY
Mathematical Physics
NEIGHBORHOODS
Mathematical physics
Mathematics
Liouville integrability
Scattering
Applied Mathematics
010102 general mathematics
37J35, 34L25, 57R22, 70F99, 70H05
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
FREEDOM
Celestial mechanics
scattering monodromy
010101 applied mathematics
Monodromy
Euler's formula
symbols
Scattering theory
FOCUS-FOCUS
Subjects
Details
- ISSN :
- 09517715
- Database :
- OpenAIRE
- Journal :
- Nonlinearity, 32(4), 1296-1326. IOP PUBLISHING LTD
- Accession number :
- edsair.doi.dedup.....70a224bc8bb5ea540c867a25259811e8
- Full Text :
- https://doi.org/10.48550/arxiv.1801.09613