On the Dimensions of Certain Incommensurably Constructed Sets
On the Dimensions of Certain Incommensurably Constructed Sets
It is known that the Hausdorff dimension of the invariant set Λt of an iterated function system F t on R depending smoothly on a parameter t varies lower-semicontinuously, but not necessarily continuously. For a specific family of systems we investigate numerically the conjecture that discontinuities in the dimension only …