6 papers
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…
A pasting lemma for Lipschitz functions
Matthew D. Kvalheim, Paul Gustafson, Samuel A. Burden
We give a necessary and sufficient condition ensuring that any function which is separately Lipschitz on two fixed compact sets is Lipschitz on their union.
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…
Gait modeling and optimization for the perturbed Stokes regime
Matthew D. Kvalheim, Brian Bittner, Shai Revzen
Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometr…
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…