## Results on Dynamical Systems, obtained at the Institute

## The inverse and direct problem of Dynamics in Celestial Mechanics.

The planar inverse problem of dynamics has been considered in inertial and rotating frames, with applications concerning Hénon-Heiles type potentials, as in

- M.-C. Anisiu, A. Pal,
*Special families of orbits for the Hénon-Heiles type potential*, Rom. Astron. J. 9 (2) (1999), 179-185. - M.-C. Anisiu, G. Bozis, Two-dimension potentials which generate spatial families of orbits, Astron. Nachr. 330 (2009), 411-415.

A self contained introduction in the planar inverse problem was presented in

- M.-C. Anisiu,
*An alternative point of view on the equations of the inverse problem of dynamics*, Inverse Problems 20 (2004), 1865-1872.

and the 3D energy-free partial differential equations were obtained in

- M.-C. Anisiu,
*The energy-free equations of the 3D inverse problem of dynamics*, Inverse Probl. Sci. Eng. 13 (2005), 545-558

We mention a survey paper and a book on this topic

- M.-C. Anisiu,
*PDEs in the inverse problem of dynamics*, Analysis and Optimization of Differential Systems, Eds. V. Barbu et al, Kluwer Academic Publishers, Boston/ Dordrecht/ London 2003, 13-20. - Mira-Cristiana Anisiu,
*The Equations of the Inverse Problem of Dynamics*, House of the Book of Science, 2003, ISBN 973-686-466-9 (in Romanian)

Programmed motion in the inverse problem of dynamics was considered in

- G. Bozis, M.-C. Anisiu, Programmed motion in the presence of homogeneity, Astron. Nachr. 330 (2009), 791-796.
- G. Bozis, M.-C. Anisiu, Programmed motion with homogeneity assumptions, Proceedings of the International Conference on the Dynamics of Celestial Bodies, 23-26 June 2008, Litohoro-Olympus, Thessaloniki, Greece, Eds. H. Varvoglis and Z. Knezevic, Beograd 2009, 83-87 (ISBN 978-960-243-664-6).

## Numerical analysis of dynamical systems.

Besides general numerical methods used in the numerical analysis of dynamical systems particularly interest was shown to simplectic methods and methods conserving differential invariants. Using such methods fairly accurate results were obtained for the N body problem with N greater than or equal to 5.

- C. I. Gheorghiu,
*Numerical Methods for Dynamical Systems*, Second Ed., Books of Science Publishing House, Cluj-Napoca, 2006, X+201 pp, ISBN 973-686-896-6 978-973-686-896-2 (in Romanian).