| Abstract: |
| The phenomenon of chaotic scattering is very relevant in different fields of science and engineering. It has been mainly studied in the context of Newtonian mechanics, where the velocities of the particles are low in comparison with the speed of light. In this talk, we analyze global properties such as the escape time distribution and the decay law of the Henon-Heiles system in the context of special relativity. Our results show that the average escape time decreases with increasing values of the relativistic factor beta. As a matter of fact, we have found a crossover point for which the KAM islands in the phase space are destroyed when beta reaches a critical value. On the other hand, the study of the survival probability of particles in the scattering region shows an algebraic decay for values of beta below of that critical value, and this law becomes exponential for beta above to that value. Surprisingly, a scaling law between the exponent of the decay law and the beta factor is uncovered where a quadratic fitting between them is found. The results of our numerical simulations agree faithfully with our qualitative arguments. Besides, we compute the basin entropy and the fractal dimension of the set of singularities of the scattering function in function of beta. This is joint work with Miguel A F Sanjuan and Juan D Bernal (Spain). |
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