Abstract
After recognizing that point particles moving inside the extended version of the rippled billiard perform Lévy flights characterized by a Lévy-type distribution with , we derive a generalized two-dimensional nonlinear map able to produce Lévy flights described by with . Due to this property, we call the Lévy map. Then, by applying Chirikov's overlapping resonance criteria, we are able to identify the onset of global chaos as a function of the parameters of the map. With this, we state the conditions under which the Lévy map could be used as a Lévy pseudorandom number generator and furthermore confirm its applicability by computing scattering properties of disordered wires.
- Received 18 June 2014
DOI:https://doi.org/10.1103/PhysRevE.90.042138
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