×
Bruschi, M.; Calogero, F.

Novel solvable variants of the goldfish many-body model. (English) Zbl 1111.70008

J. Math. Phys. 47, No. 2, 022703, 25 p. (2006).
Summary: A recent technique to identify solvable many-body problems in two-dimensional space yields, via a new twist, new many-body problems of ”goldfish” type. Some of these models are isochronous, namely their generic solutions are completely periodic with a fixed period (independent of the initial data). The investigation of the behavior of some of these isochronous systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations.

Cited in 7 Documents

MSC:

70F10 \(n\)-body problems
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics

Keywords:

isochronous model; equilibrium configurations; diophantine relations
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1063/1.532182 · Zbl 0892.58038 · doi:10.1063/1.532182
[2] DOI: 10.1063/1.532570 · Zbl 0940.70006 · doi:10.1063/1.532570
[3] DOI: 10.1016/S0167-2789(01)00160-9 · Zbl 0990.70010 · doi:10.1016/S0167-2789(01)00160-9
[4] DOI: 10.1007/3-540-44730-X · doi:10.1007/3-540-44730-X
[5] DOI: 10.1063/1.1739297 · Zbl 1071.81109 · doi:10.1063/1.1739297
[6] DOI: 10.1063/1.1809256 · Zbl 1064.70010 · doi:10.1063/1.1809256
[7] Calogero F., Proceedings of the VI International Conference on Geometry, Integrability and Quantization pp 11– (2005)
[8] DOI: 10.1088/0305-4470/35/48/310 · Zbl 1116.34319 · doi:10.1088/0305-4470/35/48/310
[9] DOI: 10.1063/1.2061547 · Zbl 1111.70009 · doi:10.1063/1.2061547
[10] Erdelyi A., Higher Transcendental Functions (1953)
[11] DOI: 10.2991/jnmp.2005.12.s1.28 · doi:10.2991/jnmp.2005.12.s1.28
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.