Circular-like Maps: Sensitivity to the Initial Conditions,   Multifractality and Nonextensivity
  We generalize herein the usual circular map by considering inflexions of arbitrary power $z$, and verify that the scaling law which has been recently proposed [Lyra and Tsallis, Phys.Rev.Lett. 80 (1998) 53] holds for a large range of $z$. Since, for this family of maps, the Hausdorff dimension $d_f$ equals unity for all $z$ values in contrast with the nonextensivity parameter $q$ which does depend on $z$, it becomes clear that $d_f$ plays no major role in the sensitivity to the initial conditions. 
Ugur Tirnakli (Ege U.), Constantino Tsallis (CBPF), Marcelo L. Lyra   (UFAL)