Map dependence of the fractal dimension deduced from iterations of circle maps (Q1112404)

Every orientation preserving circle map g with inflection points, including the maps proposed to describe the transition to chaos in phase- locking systems, gives occasion for a canonical fractal dimension D, namely that of the associated set of \(\mu\) for which \(f_{\mu}=\mu +g\) has irrational rotation number. We discuss how this dimension depends on the order r of the inflection points. In particular, in the smooth case we find numerically that \(D(r)=D(r^{-1})=r^{-1/8}.\)