Geodesics rays diverging on average on a pair of pants
Lo Cheikh, Vila Sergio
TL;DR
This paper characterizes certain geodesic rays on a pair of pants with one cusp using coding methods, and re-establishes that the Hausdorff dimension of a related set is 1/2 through explicit calculations.
Contribution
It introduces a coding characterization of limit points for geodesic rays that spend minimal time in compact regions of a pair of pants, and provides a new proof of the Hausdorff dimension result.
Findings
Hausdorff dimension of the set is 1/2
Characterization of limit points via coding methods
Reproof of the dimension result through explicit calculus
Abstract
The aim of this paper is to characterize in terms of coding a set of limit points considered in a paper of F. Riquelme and A. Velozo corresponding to geodesic rays which spend less time in any compact region of a pair of pants with one cusp. Moreover in this particular context we reprove that the Hausdorff dimension of this set is equal 1/2 by explicit calculus.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities