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Since Dmitri Anosov has proven that manifolds of negative curvature exhibit
hyperbolicity, it is natural to ask if we get similar results for manifolds of positive
curvature. Consider a Riemannian surface with non-negative Gaussian curvature,
composed of a cylinder and two hemispheres at each end. If our surface is flattened in
one direction, and we apply geodesic flow, we want to show numerically that this system
exhibits characteristics of hyperbolicity. More precisely, we will show that one Lyapunov
exponent is positive. In this talk, I will go over how the geodesic flow was numerically
approximated and how to compute the Lyapnuov exponent using an ensemble of initial
conditions.
Pizza will be served.
Geodesics on a flattened surface
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Chaotic billiard
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Colloquium sponsored by the NSM Dean's office DUSEM grant
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