__Christos Efthymiopoulos
__

Research director

Research
Center for Astronomy and Applied Mathematics, Academy of Athens

Soranou Efessiou 4, 115 27 Athens, Greece

tel: ++30 210 6597513,
fax: ++30 210 6597602

e-mail: cefthim@academyofathens.gr

__Computation of normal forms__

i) a 145 pages tutorial article on the computation and the applications of
various types of Hamiltonian normal forms (Bitkhoff, Kolmogorov, resonant and hyperbolic). Specific examples are
given with sufficient detail for self-study.

ii) Sample Mathematica
notebooks

ii) a Fortran program for normal form calculations
up to a high expansion order. The main feature of this program is a flexible
indexing function allowing one to treat systems expressed in action-angle
variables with the following features: i) arbitrary
number of degrees of freedom, ii) developments in integer or half-integer
powers of the actions, iii) user-defined domains of expansion, iv) inclusion of
terms with explicit trigonometric dependence on time and an arbitrary number of
frequencies.

__Lecture Notes on galactic dynamics__

**Part I: Lecture
Notes in Physics 729, pp. 297-389**

Introductory article to
basic notions and currently open problems of galactic dynamics, with emphasis
on the **ellipsoidal components** of
galaxies, i.e., **elliptical galaxies,
dark halos and the bulges of disk galaxies**. Treated topics include: Jeans theorem, the ‘third
integral’ of motion, the statistical mechanics of collisionless
stellar systems, main types of orbits, resonances and global dynamics, self-consistency,
the role of chaos in galaxies, numerical techniques of integration of the
N-body problem, results of N-Body simulations, secular evolution of galactic
systems under the presence of central black holes and/or central cusps.

**Part II: European Physical Journal Special Topics 186, pp.
91-122**

Dynamics of **disc
(barred/spiral) galaxies**. Definitions and general notions
on the link between observations and dynamical modeling of discs, application
of resonant Hamiltonian perturbation theory in disc resonances. Dynamics
at the Inner Lindblad resonance and orbital density
wave theory of spiral structure, barred galaxies, phase space structure, chaos
in the corotation region, invariant manifolds of
unstable periodic orbits in the vicinity of L_{1} or L_{2} and
generation of chaotic spiral patterns, vertical resonances, live halos,
multiple pattern speeds, secular evolution.

Contents:
Introduction and basic concepts, orbits and integrals, construction of equilibria, gas dynamics, spiral structure, N-body systems.