35 citations · 111 across the 11 of their papers we have counts for
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math.DS2012★ 15 cited
Stability of a 2-dimensional Mathieu-type system with quasiperiodic coefficients
Thomas Waters
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions,…
math.DS2012★ 7 cited
Non-integrability of geodesic flow on certain algebraic surfaces
Thomas Waters
This paper addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface . We prove this is th…
math.DS2011★ 9 cited
Regular and irregular geodesics on spherical harmonic surfaces
Thomas J. Waters
The behavior of geodesic curves on even seemingly simple surfaces can be surprisingly complex. In this paper we use the Hamiltonian formulation of the geodesic equations to analyze…