Finite blocking property versus pure periodicity

Details Finite blocking property versus pure periodicity Finite blocking property versus pure periodicity

2004-06-24

arxiv.org/abs/math/0406506v4

Mathematics

Dynamical Systems

16 pages, 6 figures. v4 : minor changes to take referee's suggestions into account. In particular, an appendix is added with a

Scientific paper

A translation surface S is said to have the finite blocking property if for every pair (O,A) of points in S there exists a finite number of "blocking" points B_1,...,B_n such that every geodesic from O to A meets one of the B_i's. S is said to be purely periodic if the directional flow is periodic in each direction whose directional flow contains a periodic trajectory (this implies that S admits a cylinder decomposition in such directions). We will prove that finite blocking property implies pure periodicity. We will also classify the surfaces that have the finite blocking property in genus 2: such surfaces are exactly the torus branched coverings. Moreover, we prove that in every stratum, such surfaces form a set of null measure. In the Appendix, we prove that completely periodic translation surfaces form a set of null measure in every stratum.

Affiliated with

Also associated with

No associations

Rating

Finite blocking property versus pure periodicity 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 Finite blocking property versus pure periodicity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite blocking property versus pure periodicity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206444