# 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

*Overview:*

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:

- 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)

- 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)

- 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)

- Computational
chemistry and planetary theory

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