Computer Algebra for Dynamical Systems and Celestial Mechanics

at ACA'2009 to be held at École de technologie supérieure (ÉTS), Montréal, Québec, Canada, June 25-28, 2009

Session Organizers:

Victor Edneral Moscow State University, Russia
Aleksandr Myllari University of Turku, Finland
Nikolay Vassiliev Steklov Institute of Mathematics at St.Petersburg, Russia


Celestial Mechanics and Dynamical Systems are traditional fields for applications of computer algebra. This session is intended to discuss Computer Algebra methods and modern algorithms in the study of general continuous and discrete Dynamical Systems, Ordinary Differential Equations and Celestial Mechanics.

The following topics, among others, will be considered:

1.      Stability and bifurcation analysis of dynamical systems

2.      Construction and analysis of the structure of integral manifolds

3.      Symplectic methods.

4.      Symbolic dynamics.

5.      Normal forms and programs for their computations.

6.      Deterministic chaos in dynamical systems.

7.      Families of periodic solutions.

8.      Perturbation theories.

9.      Exact solutions and partial integrals.

10.  Computation of asymptotes of solutions and its program implementation.

11.  Integrability and nonintegrability of ODEs.

12.  Computation of formal integrals.

13.  Computer algebra for celestial mechanics and stellar dynamics.

14.  Specialized computer algebra software for celestial mechanics.

15.  Topological structure of phase portraits and computer visualization.


Preliminary List of Talks:


  1. On Integrability of a Planar ODE System

(Alexander Bruno, Keldysh Institute of Applied Mathematics of RAS and Victor Edneral, Skobeltsyn Institute of Nuclear Physics of Lomonosov Moscow State University, Russia)

  1. Symbolic algorithm for generating the multistep adiabatic representation

(B.L. Markovski , O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, Joint Institute for Nuclear Research, Dubna, Russia)

  1. Formal Integral and Caustics in Dynamical Systems with Two Degrees of Freedom

(A. Mylläri, University of Turku, Finland, T. Mylläri , Åbo Akademi University, Finland, A. Rostovtsev, S. Vinitsky, Joint Institute for Nuclear Research, Dubna, Russia)

  1. Computational chemistry and planetary theory

(Michael Barnett, Brooklyn College, City University of New York (Emeritus), USA)