Ordinary Differential Equations. Normal forms and Expansions of solutions.

at ACA'2006 to be held June 26-29, 2006 in Varna, Bulgaria

Organizers:

Alexander Bruno (Keldysh Institute of Applied Mathematics, Moscow)
Victor Edneral (Lomonosov Moscow State University)

SUBJECTS OF THE SESSION

All kinds of normal forms (resonant, developed, formal, smooth, Hamiltonian, reversible and so on), their existence, properties and methods of computation.
Programs on computation of normal forms.
Computation of periodic solutions and of conditionally periodic solutions via normal form.
Computation of asymptotic expansions of solutions and its program implementation.
Search of exact solutions.
Connection between normal forms and expansions of solutions.
Integrability via normal form or solution's expansions.
Computation of formal integrals.
Applications in problems of Mathematics (Painleve equations etc.), Mechanics, Physics and so on.

Expansions of Solutions to an ODE system, 1 hour
(Alexander Bruno, Keldysh Institute of Applied Mathematics RAS, Moscow, Russia)
On Normalization and Symmetrization of Hamiltonian Systems
(Victor Zhuravlev and Alexander Petrov, Institute for Problems in Mechanics RAS, Moscow, Russia)
Search of Additional Integrals by the Normal Form Method
(Victor Edneral, Skobeltsyn Institute of Nuclear Physics, Moscow State University, Russia)
High-accurate Method for Solving the Orr-Sommerfeld Stability Equation
(Sergey Skorokhodov, Computing Center RAS, Moscow, Russia)
Studying the Influence of Higher Order Derivative Corrections in String Theory Problems by Means of Computer Algebra
(Valentina Kolybasova, Faculty of Physics, Lomonosov Moscow State University, Russia)
Asymptotical Expansions of the Solutions to the Sixth Painleve Equation
(Irina Goruchkina, Keldysh Institute of Applied Mathematics RAS, Moscow, Russia)
Finite Solutions of the N.Kowalewski Equations for Motion of a Rigid Body about a Fixed Point
(Igor Gashenenko, Institute of Applied Mathematics and Mechanics of NASU, Donetsk, Ukraine)