**George Contopoulos, Mirella Harsoula**

**Abstract:** We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic curves of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards supporting the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that chaotic orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure…..

**Conclusions**

The main conclusions of our paper are the following:

1) Stickiness of chaotic orbits close to the unstable asymptotic manifolds of various periodic orbits delays the diﬀusion of these orbits outwards and therefore modulates the shape of the spiral structure of the galaxy for more than 10 rotations of the bar, corresponding to 1/3 of the Hubble time.

2) Chaotic orbits that are limited outside corotation modulate the outer parts of the spiral structure for smaller values of Jacobi constant while orbits with greater values of Jacobi constant modulate the inner parts of the spiral structure. Moreover, in our N-body model, stickiness to resonances for smaller values of Jacobi constants lasts for longer times than stickiness for greater values of Jacobi constants.

3) Asymptotic orbits (having initial conditions on the unstable asymptotic curve of an unstable periodic orbit) stay located close to the periodic orbit for an initial interval of time, following the shape of this speciﬁc orbit, before diﬀusing from it and supporting the spiral structure. Chaotic orbits having initial conditions inside corotation modulate the envelope of the bar and the innermost spiral structure during a time interval of fast diﬀusion (≈ 1/3 of the Hubble time) and then they are diﬀused outwards with much slower rates.

4) Using a sample of sticky chaotic orbits close to a number of unstable periodic orbits inside and outside corotation, in diﬀerent energy levels, we are able to reproduce quite well the outer envelope of the bar and the spiral structure of the galaxy.

Read more: http://arxiv.org/abs/1108.5958