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math.DS2019
Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits
Matthew D. Kvalheim, Shai Revzen
We consider dynamical systems having an attracting hyperbolic fixed point or periodic orbit and prove existence and uniqueness results for (actually $C^{k,α}_{\text{loc…
math.DS2019
Families of periodic orbits: closed 1-forms and global continuability
Matthew D. Kvalheim, Anthony M. Bloch
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We be…