Prog. Theor. Phys. Vol. 87 No. 1 (1992) pp. 93-101
Many-Valuedness of First Integrals, Their Domains and Many-Valued Solutions
Department of Physics, Nagoya University, Nagoya 464-01
(Received July 12, 1991)
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.
DOI : 10.1143/PTP.87.93
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