Uncertainty dimension and basin entropy in relativistic chaotic scattering

Physical Review. E
Juan D BernalMiguel A F Sanjuán

Abstract

Chaotic scattering is an important topic in nonlinear dynamics and chaos with applications in several fields in physics and engineering. The study of this phenomenon in relativistic systems has received little attention as compared to the Newtonian case. Here we focus our work on the study of some relevant characteristics of the exit basin topology in the relativistic Hénon-Heiles system: the uncertainty dimension, the Wada property, and the basin entropy. Our main findings for the uncertainty dimension show two different behaviors insofar as we change the relativistic parameter β, in which a crossover behavior is uncovered. This crossover point is related with the disappearance of KAM islands in phase space, which happens for velocity values above the ultrarelativistic limit, v>0.1c. This result is supported by numerical simulations and by qualitative analysis, which are in good agreement. On the other hand, the computation of the exit basins in the phase space suggests the existence of Wada basins for a range of β<0.625. We also studied the evolution of the exit basins in a quantitative manner by computing the basin entropy, which shows a maximum value for β≈0.2. This last quantity is related to the uncertainty in the predict...Continue Reading

References

Aug 28, 1989·Physical Review Letters·S BleherC Grebogi
Feb 25, 1991·Physical Review Letters·Y T LauE Ott
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J AguirreM A Sanjuán
Oct 1, 1993·Chaos·Edward Ott, Tamas Tel
Jul 11, 2006·Chaos·Jesús M SeoaneYing-Cheng Lai
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jesús M SeoaneYing-Cheng Lai
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jesús M SeoaneYing-Cheng Lai
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Boon Leong Lan, F Borondo
Dec 18, 2012·Reports on Progress in Physics·Jesús M Seoane, Miguel A F Sanjuán
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juan D BernalMiguel A F Sanjuán
Nov 11, 2015·Scientific Reports·Alvar DazaJames A Yorke
Aug 16, 2016·Scientific Reports·Alvar DazaMiguel A F Sanjuán
Apr 19, 2017·Physical Review. E·Juan D BernalMiguel A F Sanjuán

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Citations

Jul 22, 2020·Physical Review. E·D S FernándezM A F Sanjuán
Nov 21, 2020·Physical Review. E·Juan D BernalMiguel A F Sanjuán

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