Structural instability of cookie-cutter sets Original Research Article

It is proved that the cookie-cutter set in RR is structurally instable in C1C1 topology, that means for the invariant set EE of the IFS {fi}i{fi}i, we can always perturb {fi}i{fi}i arbitrarily small in C1C1 topology to provide an IFS {gi}i{gi}i with its invariant set FF, such that dimHE=dimHFdimHE=dimHF and E,FE,F are not Lipschitz equivalent.