Multi-affinity and Phase Sensitivity of Strange Nonchaotic Attractors

We study the multi-affinity and phase sensitivity of strange nonchaotic attractors (SNAs) in quasiperiodically driven systems and show that the q-dependent scaling exponent eta(q), which determines the scaling of the qth correlation function of the height differences of the graph of SNAs, exhibits phase-transition-like behaviors. Furthermore, we derive hyperscaling relations, which connect two kinds of exponents characterizing the phase sensitivity and multi-affinity. We point out that these hyperscaling laws seem to be universal in SNAs.