A class of integrable Hamiltonian systems whose solutions are (perhaps) all completely periodic

Journal of Mathematical Physics

Volumn 38, Issue 11, 1997, Pages 5711-5719

  Calogero, F ^a,b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b NONE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031518164     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532182     Document Type: Article

References (15)

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2. S. N. M. Ruijsenaars and H Schneider, "A new class of integrable systems and its relation to solitons," Ann. Phys. (NY) 170, 370-405 (1986); see also S. N. M. Ruijsenaars. "Systems of Calogero-Moser type," in Proceedings of the 1994 Banff Summer School on "Particles and Fields," CRM Proceedings and Lecture Notes (in press), and the papers referred to there.
3. M. Bruschi and F. Calogero, "The Lax representation for an integrable class of relativistic dynamical systems," Commun. Math. Phys. 109, 481-492 (1987). The following misprints in this paper should be corrected as follows: in (4.4b), replace c with - ζ(μ): inside the square bracket in the right-hand side of (4.4c), insert + p; in (4.6a) and (4.7a), omit the formulas assigning a value to c; in (4.10), multiply the right-hand side by λ.
4. M. Bruschi and F. Calogero, "General analytic solutions of certain functional equations of addition type," SIAM J. Math. Anal. 21, 1019-1030 (1990).
5. F. Calogero, "Some applications of a convenient finite-dimensional matrix representation of the differential operator," in Proceedings of the International Conference on "Special Functions: Theory and Computation," Rend. Sem. Mat., Univ. Polit. Torino, October 1984 (special issue), pp. 23-61 (see in particular Sec. 3.3); F. Calogero and M. C. Nucci, "Lax pairs galore," J. Math. Phys. 32, 72-74 (1991).
6. F. Calogero, "Some applications of a convenient finite-dimensional matrix representation of the differential operator," in Proceedings of the International Conference on "Special Functions: Theory and Computation," Rend. Sem. Mat., Univ. Polit. Torino, October 1984 (special issue), pp. 23-61 (see in particular Sec. 3.3); F. Calogero and M. C. Nucci, "Lax pairs galore," J. Math. Phys. 32, 72-74 (1991).
7. F. Calogero, "Motion of poles and zeros of nonlinear and linear partial differential equations, and related solvable many-body problems," Nuovo Cimento B 43, 177-241 (1978).
8. F. Calogero, "A solvable N-body problem in the plane. I," J. Math. Phys. 37, 1735-1759 (1996).
9. F. Calogero: "Solvable (nonrelativistic, classical) n-body problems on the line. II," J. Math. Phys. 34, 5659-5670 (1996).
10. H. Schneider, "Integrable relativistic n-particle systems in an external potential," Physica D 26, 203-209 (1987).
11. J. F. van Diejen, "Integrability of difference Calogero-Moser systems," J. Math. Phys. 35, 2983-3004 (1994); "Difference Calogero-Moser systems and finite Toda chains," J. Math. Phys. 36, 1299-1323 (1995); "Families of commuting difference operators," Ph.D. thesis, University of Amsterdam. 28 June 1994.
12. J. F. van Diejen, "Integrability of difference Calogero-Moser systems," J. Math. Phys. 35, 2983-3004 (1994); "Difference Calogero-Moser systems and finite Toda chains," J. Math. Phys. 36, 1299-1323 (1995); "Families of commuting difference operators," Ph.D. thesis, University of Amsterdam. 28 June 1994.
13. J. F. van Diejen, "Integrability of difference Calogero-Moser systems," J. Math. Phys. 35, 2983-3004 (1994); "Difference Calogero-Moser systems and finite Toda chains," J. Math. Phys. 36, 1299-1323 (1995); "Families of commuting difference operators," Ph.D. thesis, University of Amsterdam. 28 June 1994.
14. F. Calogero, "Tricks of the trade: Relating and deriving solvable and integrable dynamical systems," in Proceedings of the Workshop on Calogero-Moser-Sutherland models, CRM Series in Mathematical Physics (Springer, New York, to be published).
15. F. Calogero and J.-P. Françoise (unpublished).