caa a22 4500 475839609 CHVBK 20180406123857.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1023/A:1006425609939 doi (NATIONALLICENCE)springer-10.1023/A:1006425609939 On the Weak Kowalevski-Painlevé Property for Hyperelliptically Separable Systems [Elektronische Daten] [S. Abenda, Yu. Fedorov] We consider so called hyperelliptically separable systems (h.s.s.) arising in various physical problems, whose generic invariant manifolds can be completed either to hyperelliptic Jacobians or to their nonlinear subvarieties (strata) or their finite coverings. In the case of strata the algebraic geometrical structure of such systems has much in common with that of algebraic completely integrable systems (a.c.i.s.). Using this property we study formal singular solutions of a.c.i.s. and h.s.s., which may contain fractional powers of time. We give estimates for the number and leading behavior of their principal and lower balances both for a generic and for the so called physical direction of the flow. This can be regarded as an useful extension of the Kowalevski-Painlevé integrability test. We also prove that when the system is h.s. but not a.c.i., its generic solutions are single-valued on an infinitely sheeted ramified covering of the complex time plane. Some model examples are considered, such as the hierarchy of integrable generalizations of the Henon-Heiles and the Neumann systems. Kluwer Academic Publishers, 2000 Painlevé analysis nationallicence Jacobian varieties nationallicence integrable systems nationallicence Abenda S. Dipartimento di Matematica and C.I.R.A.M., Università degli studi di Bologna, 40123, Bologna, Italy aut Fedorov Yu Department of Mathematics and Mechanics, Moscow Lomonosov University, Vorobievy Gory, 119899, Moscow, Russia aut Acta Applicandae Mathematica Kluwer Academic Publishers 60/2(2000-01-01), 137-178 0167-8019 60:2<137 2000 60 10440 https://doi.org/10.1023/A:1006425609939 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006425609939 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abenda S. Dipartimento di Matematica and C.I.R.A.M., Università degli studi di Bologna, 40123, Bologna, Italy aut NATIONALLICENCE 700 1- Fedorov Yu Department of Mathematics and Mechanics, Moscow Lomonosov University, Vorobievy Gory, 119899, Moscow, Russia aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 60/2(2000-01-01), 137-178 0167-8019 60:2<137 2000 60 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer