| DATE: |
2006-04-18 15:00 - |
| PLACE: |
Build. No.4, 1F, Seminar hall |
| TITLE: |
A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem |
| CONTACT: |
tsuda |
| SPEAKER: |
Dr. Francesco Calogero (Univ. of Rome) |
| LANGUAGE: |
English |
| ABSTRACT: |
A (somewhat novel) technique to identify and investigate solvable many-body problems is described, and it is shown that it reproduces some standard many-body problems already known to be integrable and solvable, as well as some new ones. Some of these new 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 systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations.
References: F. Calogero and J.-P. Francoise, "New solvable many-body problems in the plane", J. Nonlinear Math. Phys. (in press). F. Calogero, "A technique to identify solvable dynamical systems, and a solvable generalization of the goldfish many-body problem", J. Math. Phys. 45, 2266-2279 (2004); "A technique to identify solvable dynamical systems, and another solvable extension of the goldfish many-body problem", J. Math. Phys. 45, 4661-4678 (2004). F. Calogero and S. Iona, "Novel solvable extension of the goldfish many-body model", J. Math. Phys. 46, 103515 (2005). M. Bruschi and F. Calogero, "Novel solvable variants of the goldfish many-body model", J. Math. Phys. (in press); "Goldfishing", (in preparation). F. Calogero and E. Langmann, "Goldfishing via gauge transformations", (in preparation).
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