4 papers · 1 filter
Estimating Phase from Observed Trajectories Using the Temporal 1-Form
Simon Wilshin, Matthew D. Kvalheim, Clayton Scott +1
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asympto…
Conley's fundamental theorem for a class of hybrid systems
Matthew D. Kvalheim, Paul Gustafson, Daniel E. Koditschek
We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a glo…
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…
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…