Laboratoire de Physique Théorique
Toulouse - UMR 5152

Chaotic scattering in open Hamiltonian systems subjected to different kind of perturbations is not only of fundamental interest but also important for problems of current concern in applications. The Henon-Heiles Hamiltonian as a paradigm of open Hamiltonian systems is considered in the presence of different kinds of perturbations as dissipation, noise and periodic forcing, which are very typical in different physical situations. The effects of these perturbations on the escaping dynamics and on the topology of the basins associated to the phase space and to the physical space are considered. We have also found, in presence of a periodic forcing, an exponential-like decay law for the survival probability of the particles in the scattering region where the frequency of the forcing plays a crucial role. For very weak noises we find long transients for the time escape distributions and a decay law algebraic. We also compare the obtained results for the dissipative, noisy and periodic forcing case. We expect all this work to be useful for a better understanding of the escapes in open Hamiltonian systems in the presence of different kinds of perturbations.

References
[1] J. Seoane, Jacobo Aguirre, Miguel A. F. Sanjuan, and Ying-Cheng Lai. Basin Topology in Dissipative Chaotic Scattering. Chaos 16, 023101, 2006.
[2] J. Seoane, Miguel A. F. Sanjuan, and Ying-Cheng Lai. Fractal dimension in dissipative chaotic scattering. Phys. Rev. E 76, 016208, 2007.
[3] Jesus Seoane, Liang Huang, Miguel A. F. Sanjuan, and Ying-Cheng Lai. Effect of noise on chaotic scattering. Phys. Rev. E 79, 047202, 2009.
[4] Fernando Blesa, Jesus Seoane, Roberto Barrio, and Miguel A. F. Sanjuan. To escape or not to escape, that is the question : Perturbing the Hnon-Heiles Hamiltonian. Int. J. Bifurcation and Chaos 22, 1230010, 2012.
[5] J. Seoane and Miguel A. F. Sanjuan. New Developments in Classical Chaotic Scattering. Rep. Prog. Phys. 76, 016001, 2013.
[6] Juan D. Bernal, Jesus M. Seoane, and Miguel A. F. Sanjuan. Weakly noisy chaotic scattering. Physical Review E 88, 032914, 2013.
[7] Fernando Blesa, Jesus Seoane, Roberto Barrio, and Miguel A. F. Sanjuan. Effects of periodic forcing in chaotic scattering. Phys. Rev. E 89, 042909, 2014.