Two-dimensional nonlinear map characterized by tunable Levy flights

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processo FAPESP: 2013/14655-9

Processo FAPESP: 2014/18672-8

Processo FAPESP: 2012/23688-5

After recognizing that point particles moving inside the extended version of the rippled billiard perform Levy flights characterized by a Levy-type distribution P(l) similar to l(-(1+alpha)) with alpha = 1, we derive a generalized two-dimensional nonlinear map M alpha able to produce Levy flights described by P(l) with 0 < alpha < 2. Due to this property, we call M alpha the Levy map. Then, by applying Chirikov&apos;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 Levy map could be used as a Levy pseudorandom number generator and furthermore confirm its applicability by computing scattering properties of disordered wires.