Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry

• Autorzy: Alexander D. Bruno
• Języki publikacji: EN

Abstrakty

EN

Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local integrability of a planar ODE system. In Section 5, we expound the spacial generalizations of planar constructions. Power Geometry gives alternatives to some methods of Algebraic Geometry, Differential Algebra, Nonstandard Analysis, Microlocal Analysis, Group Analysis and to other algebraic methods in Dynamical Systems.

Kategorie tematyczne

• 37G05: Normal forms
• 34E05: Asymptotic expansions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 94
• Numer: 1
• Strony: 83-98

Daty

wydano

2011

Twórcy

autor

Alexander D. Bruno

• Keldysh Institute of Applied Mathematics and, Lomonosov Moscow State University, Moscow, Russia

Identyfikatory

DOI

10.4064/bc94-0-4