## Overview

Celestial Mechanics and Dynamical Systems are traditional fields for applications of computer algebra. Computer algebra methods play a fundamental role in the treatment of concrete problems and applications. Characteristically, even for seemingly small problems, the computations may become very involved. Computer algebra applications include nontrivial use of existing systems such as Maple, Mathematica or Singular and the development and implementation of new algorithms, and complete specialized packages.

The session will bring together specialists from diverse application areas, differential equations, dynamical systems and algebra.

In particular the following topics will be considered:

- Stability and bifurcation analysis of dynamical systems
- Construction and analysis of the structure of integral manifolds
- Symplectic methods.
- Symbolic dynamics.
- Normal form theory and normal form computations.
- Deterministic chaos in dynamical systems.
- Families of periodic solutions.
- Perturbation theories and reductions.
- Exact solutions and partial integrals.
- Analysis and blow-ups of non-elementary stationary points.
- Geometric singularities of implicit ordinary differential equations.
- Analysis of singularities of equations.
- Computation of asymptotic forms and asymptotic expansions of solutions and their program implementation.
- Integrability and nonintegrability of ODEs; in particular algebraic invariant sets and Darboux integrability.
- Discrete Dymanical Systems.
- 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.
- Specialized software for planar systems.

For earlier sessions on Celestial Mechanics see the history page of ACA