Computer Algebra for Dynamical Systems and Celestial Mechanics

at ACA'2008 to be held at RISC, Linz, Austria (July 27-30)

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:

Stability and bifurcation analysis of dynamical systems

Construction and analysis of the structure of integral manifolds

Symplectic methods.

Symbolic dynamics.

Normal forms and programs for their computations.

Deterministic chaos in dynamical systems.

Families of periodic solutions.

Perturbation theories.

Exact solutions and partial integrals.

Analysis of singularities of equations by power geometry algorithms.

Computation of asymptotic forms and asymptotic expansions of solutions and its program implementation.

Integrability and nonintegrability of ODEs.

Computation of formal integrals.

Computer algebra for celestial mechanics and stellar dynamics.

Specialized computer algebra software for celestial mechanics.

Topological structure of phase portraits and computer visualization.

(new) The Program (pdf, html)


The Initial List of Talks:

  1. Analysis of dynamics for a satellite with gyros with the aid of the software LinModel
    (Andrey V. Banshchikov, Institute for System Dynamicsand Control Theory, SB of RAS, Russia)
  2. A modern, generic and object-oriented algebraic manipulation framework for Celestial Mechanics
    (Francesco Biscani, Department of Astronomy, University of Padua, Italy)
  3. Application of the computer algebra system PSP to the Earth's rotation problem
    (V.A. Brumberg, T.V.Ivanova, Institute of Applied Astronomy, St.-Petersburg, Russia)
  4. On gyroscopic stabilization with the singular matrix of gyroscopic forces
    (Larisa A. Burlakova, Institute of Systems Dynamics and Control Theory, SB of RAS, Russia)
  5. Calculation of the asymptotic expansion of continuous spectrum solutions of the two-dimentional boundary problem
    (O. Chuluunbaatar, V.P. Gerdt, A.A. Gusev, S.I. Vinitsky, Joint Institute for Nuclear Research, Dubna, Russia,
    , Institute of Nuclear Physics, Almaty, Kazakhstan)
  6. Construction of periodic orbits and their regularity as approximation of invariant curves
    (Corrado Falcolini, University of Roma Tre
    , Italy)
  7. Approximating center manifolds on a model for a Solar Sail
    (Ariadna Farrés and Àngel Jorba, Departament de Matemàtica Aplicada i Anàlisi Universitat de Barcelona, Spain)
  8. On invariant manifolds of conservative systems with 3-rd and 6-th degree first integrals
    (Valentine D. Irtegov, Tatiana N. Titorenko, Institute for Systems Dynamics and Control Theory, SB of RAS, Russia)
  9. On the automatic computation of high order variationals for the numerical integration of ODE by means of the Taylor method
    (Àngel Jorba, Departament de Matemàtica Aplicada i Anàlisi Universitat de Barcelona, Spain)
  10. Planetary three-body problem with Poisson series processor
    (K.V. Kholshevnikov, Sobolev Astronomical Institute, St.Petersburg State University, Russia,
    E.D. Kuznetsov, Astronomical Observatory, Ural State University, Russia)
  11. Nekhoroshev estimates in a symplectic mapping model of the 1:1 resonance of the elliptic restricted three body problem
    (Christoph Lhotka, Institute for Astronomy, University of Vienna, Austria)
  12. Dynamic visualization for computational dynamics
    (Daniel Lichtblau, Wolfram Research, USA)
  13. Symbolic creation of nilpotent normal forms: another point of view
    (J. Mikram and F. Zinoun, University of Rabat and University of Meknès
    , Moroccan Kingdom)
  14. Caustics in the Dynamical Systems with Two Degrees of Freedom
    (A. Mylläri, University of Turku, Finland,
    T. Mylläri
    , Åbo Akademi University, Finland,
    A.Gusev , S. Vinitsky, Joint Institute for Nuclear Research, Dubna
    , Russia)
  15. PPKBZ9: Symbolic-numeric model in artificial satellite theory
    (Juan F. San-Juan, Dept. Matemáticas y Computación, Universidad de La Rioja, Spain)
  16. Wave fronts and caustics of vector fields
    (Victor Varin, Keldysh Institute of Applied Mathematics, Moscow, Russia)
  17. On Complexity of Series Manipulations in Celestial Mechanics
    (Nikoly Vassiliev, Steklov Institute of Mathematics at St. Petersburg, Russia)


Important Dates:

  • May 26, 2008: Deadline for submissions of extended abstracts (as PDF files, not more than 4 pages in A4). Abstracts should include the title, authors' name(s), affiliation(s) and the contact e-mail. Send them to Victor Edneral, please.
  • June 02, 2008: Notification of Acceptance.