Session Organizers:
· Raya Khanin,
This
session is intended to discuss Computer Algebra methods and algorithms in the
study of Dynamical Systems. The session will also focus on important
applications of Computer Algebra to Dynamical Systems arising in many areas of
science and engineering.
Since
nonlinear Dynamical Systems cannot be exactly solved in general, the role of
Computer Algebra in finding approximate solutions as well as in the
pre-analysis for the numerical methods, is extremely
important. From this point of view, the construction of exact or approximate
solutions in symbolic form constitutes the most powerful approach to study the
behavior of Dynamical Systems. Computer Algebra methods have also emerged as
powerful tools in investigating stability and bifurcations.
Topics:
·
Stability
and bifurcation analysis of dynamical systems.
· Investigation of limit cycles.
· Symbolic integration of ODEs.
·
Construction
and analysis of the structure of integral manifolds.
·
Construction
of approximate solutions in symbolic form.
· Construction of normal forms.
·
Construction
and investigation of formal integrals of dynamical systems.
· Non-Holonomic systems.
·
Construction
of integral invariants and partial integrals.
· Invariants of symplectic mapping.
·
Symplectic
integration of hamiltonian systems.
· Semi-numerical algorithms.
· Symbolic dynamics.
·
Applications
of computer algebra methods to celestial mechanics.
·
Computer
algebra software and and special-purpose packages.
·
Applications
to control theory and mechanical engineering.
· Discrete simulation and automata theory
Preliminary
program:
Session Organizers:
The aim of the session is to provide a forum
for discussing new computer algebra algorithms, techniques, software systems
and applications in the fields of celestial mechanics and gravitational
physics. Although these two research fields are rather different, there are
many computer algebra ideas and techniques common to both fields, and it seems
to be quite interesting to discuss these questions in such an audience.
Both celestial mechanics and relativistic
gravity theories are traditional application fields of computer algebra. Both
fields are known for their extremely complicated calculations with many thousands
of terms. The complexity of calculations in both research fields forces to
develop specialized algorithms and specialized highly optimized software
systems. Poisson series processors optimized for typical applications in
celestial mechanics and specialized systems for tensorial calculations in
relativity play a very important role. However, also general-purpose systems
can be successfully used in many cases.
The session is intended to cover the whole
spectrum of computer algebra techniques and applications in celestial mechanics
and gravitational physics. Session topics include (but are not restricted to):
A.1 Specialized computer algebra
systems for celestial mechanics
A.2 Applications of
general-purpose computer algebra systems in celestial mechanics
A.3 Algorithm design in celestial
mechanics
B.1 Computer algebra systems for
gravitational physics
B.2 Algorithms for tensorial
computations
B.3 Applications of computer
algebra in gravitational physics
AB.1 Computer algebra in teaching
celestial mechanics and general relativity
AB.2 Symbolic-numeric interface