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Astron. Astrophys. 344, 879-890 (1999)

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Imperfect fractal repellers and irregular families of periodic orbits in a 3-D model potential

B. Barbanis, H. Varvoglis and Ch.L. Vozikis

Section of Astrophysics, Astronomy and Mechanics, Department of Physics, Aristotle University of Thessaloniki, GR-540 06 Thessaloniki, Greece

Received 2 July 1998 / Accepted 1 February 1999


A model, plane symmetric, 3-D potential, which preserves some features of galactic problems, is used in order to examine the phase space structure through the study of the properties of orbits crossing perpendicularly the plane of symmetry. It is found that the lines formed by periodic orbits, belonging to Farey sequences, are not smooth neither continuous. Instead they are deformed and broken in regions characterised by high Lyapunov Characteristic Numbers (LCN's). It is suggested that these lines are an incomplete form of a fractal repeller, as discussed by Gaspard and Baras (1995), and are thus closely associated to the "quasi-barriers" discussed by Varvoglis et al. (1997). There are numerical indications that the contour lines of constant LCN's possess fractal properties. Finally it is shown numerically that some of the periodic orbits -members of the lines- belong to true irregular families. It is argued that the fractal properties of the phase space should affect the transport of trajectories in phase or action space and, therefore, play a certain role in the chaotic motion of stars in more realistic galactic potentials.

Key words: chaos – celestial mechanics, stellar dynamics – Galaxy: kinematics and dynamics – galaxies: kinematics and dynamics

Send offprint requests to: H. Varvoglis (varvogli@astro.auth.gr)

© European Southern Observatory (ESO) 1999

Online publication: March 29, 1999