Cantor sets of low density and Lipschitz functions on C1 curves

Surjective Functions on Computably Growing Cantor Sets

Every in nite binary sequence is Turing reducible to a random one. This is a corollary of a result of P eter G acs stating that for every co-r.e. closed set with positive measure of in nite sequences there exists a computable mapping which maps a subset of the set onto the whole space of in nite sequences. Cristian Calude asked whether in this result one can replace the positive measure conditi...

Dimension Functions of Cantor Sets

We estimate the packing measure of Cantor sets associated to nonincreasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets.

Cantor Sets, Binary Trees and Lipschitz Circle Homeomorphisms

We define the notion of rotations on infinite binary trees, and construct an irrational tree rotation with bounded distortion. This lifts naturally to a Lipschitz circle homeomorphism having the middle-thirds Cantor set as its minimal set. This degree of smoothness is best possible, since it is known that no C1 circle diffeomorphism can have a linearly self-similar Cantor set as its minimal set.

Uncountably Many Inequivalent Lipschitz Homogeneous Cantor Sets in Ir

Null Sets and Essentially Smooth Lipschitz Functions

In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this deenition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.