Singularity spectrum for period n-tupling in area-preserving maps

The singularity spectrum f(α) and the generalized dimension D(q) of the critical orbit is numerically obtained to study the global scaling behavior of period n-tupling (n = 2,3,4) in area-preserving maps. It is found that f(α) becomes quite different as n is changed, and the generalized dimension D(q) increases for all q as n increases. The global scaling behavior of conservative systems is different from that of dissipative systems. Moreover, for conservative systems, the global scaling behavior seems to depend on dimensionality