Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4627963 | Applied Mathematics and Computation | 2014 | 6 Pages |
Abstract
Some statistical and dynamical properties for the problem of relativistic charged particles in a wave packet are studied. We show that the introduction of dissipation change the structure of the phase space and attractors appear. Additionally, by changing at least one of the control parameters, the unstable manifold touches the stable manifold of the same saddle fixed point and a boundary crisis occurs. We show that the chaotic attractor is destroyed given place to a transient which follows a power law with exponent -1 when varying the control parameters near the criticalities. On the other hand, by changing at least two control parameters and by using the Lyapunov exponents to classify orbits with chaotic and periodic behaviour, we show the existence of infinite shrimp-shaped domains, which correspond to the periodic attractors, embedded in a region with chaotic behaviour. Finally, we show the first indication of a shrimp in a three dimension parameter space.
Keywords
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Matheus Hansen, Diogo R. da Costa, Diego F.M. Oliveira, Edson D. Leonel,