Scaling properties for a family of discontinuous mappings

• We study scaling properties of a family of nonlinear discontinuous maps.
• This family is the discontinuous-map representation of well-known nonlinear systems.
• The exponent characterizing the family of maps defines universality classes.

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 γγ 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 γγ; therefore classes of universality can be defined. For specific values of γγ 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.