Two-dimensional nonlinear map characterized by tunable Lévy flights.
After recognizing that point particles moving inside the extended version of the rippled billiard perform Lévy flights characterized by a Lévy-type distribution P(l)∼l(-(1+α)) with α=1, we derive a generalized two-dimensional nonlinear map Mα able to produce Lévy flights described by P(l) with 0<α<2. Due to this property, we call Mα 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.
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
J A
JA
Méndez-Bermúdez
UNESP - Univ Estadual Paulista, Campus São João da Boa Vista, São João da Boa Vista, São Paulo 13874-149, Brazil.
Juliano A
JA
de Oliveira
Departamento de Física, UNESP - Univ Estadual Paulista, Avenida 24A, 1515 Bela Vista, Rio Claro, São Paulo 13506-900, Brazil.
Edson D
ED
Leonel