caa a22 4500 445835893 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0669-6 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0669-6 Integrability of Hamiltonian systems and transseries expansions [Elektronische Daten] [Werner Balser, Masafumi Yoshino] This paper studies analytic Liouville-nonintegrable and C ∞-Liouville-integrable Hamiltonian systems with two degrees of freedom. We prove the property for a class of Hamiltonians more general than the one studied in Gorni and Zampieri (Differ Geom Appl 22:287-296, 2005). We also show that a certain monodromy property of an ordinary differential equation obtained as a subsystem of a given Hamiltonian and the transseries expansion of a first integral play an important role in the analysis (cf. (4)). In the former half the analytic Liouville-nonintegrability for a class of Hamiltonians satisfying the above condition is shown. For these analytic nonintegrable Hamiltonians one cannot construct nonanalytic first integrals concretely as in Gorni and Zampieri (Differ Geom Appl 22:287-296, 2005). In the latter half, the nonanalytic integrability from the viewpoint of a transseries expansion of a first integral is discussed. More precisely, we construct a first integral in a formal transseries expansion in a general situation. Then we show convergence of transseries or existence of the first integral being asymptotically equal to a given formal transseries solution. Springer-Verlag, 2010 Nonintegrability nationallicence Hamiltonian systems nationallicence Transseries nationallicence Summability nationallicence Balser Werner Institut für Angewandte Analysis, Universität Ulm, 89069, Ulm, Germany aut Yoshino Masafumi Department of Mathematics, Hiroshima University, 739-8526, Higashi-Hiroshima, Japan aut Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 257-280 0025-5874 268:1-2<257 2011 268 209 https://doi.org/10.1007/s00209-010-0669-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0669-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balser Werner Institut für Angewandte Analysis, Universität Ulm, 89069, Ulm, Germany aut NATIONALLICENCE 700 1- Yoshino Masafumi Department of Mathematics, Hiroshima University, 739-8526, Higashi-Hiroshima, Japan aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 257-280 0025-5874 268:1-2<257 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer