Scaling properties for a family of discontinuous mappings - Méndez-Bermúdez, J. A.; De Oliveira, Juliano A. [UNESP]; Aguilar-Sánchez, R.; Leonel, Edson D. [UNESP] (Elsevier, 2015)
Scaling exponents that describe a transition from integrability to non-integrability in a family of two-dimensional, nonlinear, and discontinuous mappings are obtained. The mapping considered is parameterized by the exponent γ in the action variable. The scaling exponents describing the behavior of the average square action along the chaotic orbits are obtained for different values of γ; therefore classes of universality can be defined. For specific values of γ our mapping acts as the discontinuous-map representation of well-known nonlinear systems, thus making our study broadly applicable. Also, the formalism used is general and the procedure can be extended to characterize many other dynamical systems.
Keywords: Discontinuous function; Nonlinear map; Scaling laws