4 citations · 6 across the 9 of their papers we have counts for
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…
Challenges in Dynamic Mode Decomposition
Ziyou Wu, Steven L. Brunton, Shai Revzen
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide ran…
Representing and computing the B-derivative of an vector field's flow
George Council, Shai Revzen, Samuel A. Burden
This paper concerns the first-order approximation of the piecewise-differentiable flow generated by a class of nonsmooth vector fields. Specifically, we represent and compute the B…
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…