Cantor sets in the line: scaling function and the smoothness of the shift map

Details Cantor sets in the line: scaling function and the smoothness of the shift map Cantor sets in the line: scaling function and the smoothness of the shift map

1992-04-20

arxiv.org/abs/math/9204241v1

Mathematics

Dynamical Systems

Scientific paper

Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map are defined is a Cantor set. Associated to the construction of this Cantor set is the scaling function which records the infinitely deep geometry of this Cantor set. This scaling function is an invariant of $C^1$ conjugation. We solve the inverse problem posed by Dennis Sullivan: given a scaling function, determine the maximal possible smoothness of any expanding map which produces it.

Affiliated with

Also associated with

No associations

Rating

Cantor sets in the line: scaling function and the smoothness of the shift map does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cantor sets in the line: scaling function and the smoothness of the shift map, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cantor sets in the line: scaling function and the smoothness of the shift map will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-619861