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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Article

Normally generated line bundle and laurent series solutions of nonlinear differential equations

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pp. 151–171Vol. 16Issue 2July 2018DOI: 10.1080/1726037X.2018.1437941XML
Received:
08 Feb 2017
Accepted:
24 Sep 2017
Published Online:
30 Oct 2018
Article type:
Article
Language:
EN
Article no.:
1726037X.2018.1437941
Pages:
151–171

Abstract

The aim of this paper is to demonstrate the rich interaction between the properties of dynamical systems, the geometry of its asymptotic solutions, and the theory of Abelian varieties. We are going to illustrate as well that the nature of many methods for finding solutions of some dynamical systems is determined by the Laurent series for solutions of nonlinear differential equations. We apply the methods to the Kowalewski’top a solid body rotating about a fixed point, the Kirchhoff’s equations of motion of a solid in an ideal fluid and the Ramani-Dorizzi-Grammaticos (RDG) series of integrable potentials.

Keywords

Differential equationsMeromorphic solutionsAbelian varietiesJacobiansPrym varietiesIsogenyIntegrable systems

Subject Classifications

34M4534M0511G1014H4014K0214H70

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