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


Curriculum Vitae


Conferences and seminars

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 L1 or L2 and generation of chaotic spiral patterns, vertical resonances, live halos, multiple pattern speeds, secular evolution.


Scholarpedia article: G. Contopoulos and C. Efthymiopoulos: 2011, “Galactic Dynamics”, Scholarpedia 6(5):10670

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