Presentation Title

Linear Trajectories on Homothety Surfaces

Faculty Mentor

Joshua Bowman

Start Date

18-11-2017 10:45 AM

End Date

18-11-2017 11:00 AM

Location

9-285

Session

Physical Sciences 2

Type of Presentation

Oral Talk

Subject Area

physical_mathematical_sciences

Abstract

A homothety surface is constructed by gluing the sides of polygons in the plane by homotheties—compositions of scalings and translations. Homothety surfaces generalize translation surfaces, which have been well-studied for several decades. We examine long-term behaviors of periodic and non-periodic linear trajectories on a one-parameter family of genus-2 homothety surfaces and compare these trajectories with those on the square torus.

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Nov 18th, 10:45 AM Nov 18th, 11:00 AM

Linear Trajectories on Homothety Surfaces

9-285

A homothety surface is constructed by gluing the sides of polygons in the plane by homotheties—compositions of scalings and translations. Homothety surfaces generalize translation surfaces, which have been well-studied for several decades. We examine long-term behaviors of periodic and non-periodic linear trajectories on a one-parameter family of genus-2 homothety surfaces and compare these trajectories with those on the square torus.