Abstract
This paper can be considered as a remark to the old Jacobi paper [1] about the quadruple periodic functions. The reason to come back to Jacobi has appeared in connection with the following integrable dynamical system.
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References
C. G. Jacobi, De functionibus duarum variabilum quadrupliciter periodicis quibus theoria transcendentium Abelinarium innititur, Crelle J., b.13 (1835).
C. G. Jacobi, “Forlesungen über Dynamik”, Berlin, 1884.
Chang S.-J., Shi K.J., Billiard system on qudratic surfaces and the Poncelet theorem, J. Math. Phys., n.1 (1989), pp. 788–804.
M. Adler, P. van Moerbeke, Algebraic integrable system. A systematic approach, Perspectives in Math.-Boston, AP, 1989.
P. Griffiths, A variation on the theorem of Abel, Invent. Math., vol. 35 (1976), pp. 321–390.
A. P. Veselov, Integrable mappings, Russ.Math.Surv., vol. 46, n.5 (1991), pp. 3–45 (In Russian).
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© 1994 Springer Basel AG
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Veselov, A.P. (1994). Complex Geometry of the Billiard on the Ellipsoid and Quasicrystallic Curves. In: Kuksin, S., Lazutkin, V., Pöschel, J. (eds) Seminar on Dynamical Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 12. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7515-8_22
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DOI: https://doi.org/10.1007/978-3-0348-7515-8_22
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-7515-8
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