Quick Search:
Prog. Theor. Phys. Vol. 87 No. 1 (1992) pp. 93-101
Many-Valuedness of First Integrals, Their Domains and Many-Valued Solutions
Masaharu Ishii
Department of Physics, Nagoya University, Nagoya 464-01
(Received July 12, 1991)
Abstract:
Many-valuedness of first integral is studied through the 2-dimension Lotka-Volterra model and it is proved that this many-valuedness brings nonexistence of the Puiseux expansions of the general solutions. In other words, a system with a certain many-valued first integral does not have the weak Painlevé property. This implies that many-valuedness is necessary for their general solutions. In physical case, we consider the influence of the logarithmic branchings of first integrals on real motion and show that a first integral including logarithmic functions becomes single-valued almost everywhere in the real domain under a certain condition of singularity sets of the first integral.
URL :
http://ptp.ipap.jp/link?PTP/87/93/
DOI : 10.1143/PTP.87.93
References:
-
M. Tabor and J. Weiss, Phys. Rev. A24 (1981), 2157[APS].
-
Y. F. Chang, M. Tabor and J. Weiss, J. Math. Phys. 23 (1982), 531[CrossRef].
- S. L. Ziglin, Trans. Moscow Math. Soc. 1 (1982), 283.
-
T. Bountis, V. Papageorgiou and M. Bier, Physica 24D (1987), 292[Elsevier].
-
J. D. Fournier, G. Levine and M. Tabor, J. of Phys. A21 (1988), 33[IoP STACKS].
- W. -H. Steeb, M. Kloke, B. M. Spieker and A. Kunick, Found. Phys. 15 (1985), 637.
-
A. Ramani, B. Grammaticos and T. Bountis, Phys. Rep. 180 (1989), 159[CrossRef].
- M. Ishii, Prog. Theor. Phys. 84 (1990), 386[PTP].
- M. Ishii, “The Necessary Condition for Algebraic Integrability of Dynamical Systems with Dominants”, Preprint, 1990.
