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math.DS2023★ 2 cited
Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria
Philip Arathoon, Matthew D. Kvalheim
A frequently repeated claim in the "applied Koopman operator theory'' literature is that a dynamical system with multiple isolated equilibria cannot be linearized in the sense of a…
math.DS2023★ 4 cited
Linearizability of flows by embeddings
Matthew D. Kvalheim, Philip Arathoon
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on…
math.DS2019
Singular Reduction of the 2-Body Problem on the 3-Sphere and the 4-Dimensional Spinning Top
Philip Arathoon
We consider the dynamics and symplectic reduction of the 2-body problem on a sphere of arbitrary dimension. It suffices to consider the case for when the sphere is 3-dimensional an…