Linear Trajectories on Homothety Surfaces
Presentation Type
Poster
Keywords
topology dynamical systems linear trajectories homothety surfaces mathematics math
Department
Mathematics
Major
Mathematics
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.
Faculty Mentor
Joshua Bowman
Funding Source or Research Program
Summer Undergraduate Research Program, Undergraduate Research Fellowship
Location
Waves Cafeteria
Start Date
23-3-2018 2:00 PM
End Date
23-3-2018 3:30 PM
Linear Trajectories on Homothety Surfaces
Waves Cafeteria
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.