The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …

We establish the convergence of a class of numerical algorithms, known as dynamic mode
decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite …

Koopman operators globally linearize nonlinear dynamical systems and their spectral
information is a powerful tool for the analysis and decomposition of nonlinear dynamical …

We study a class of dynamical systems modelled as stationary Markov chains that admit an
invariant distribution via the corresponding transfer or Koopman operator. While data-driven …

Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which
computes generalized eigenfunction decompositions of Koopman operators. By considering …

Starting from measured data, we develop a method to compute the fine structure of the
spectrum of the Koopman operator with rigorous convergence guarantees. The method is …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

Dynamical systems provide a comprehensive way to study complex and changing behaviors
across various sciences. Many modern systems are too complicated to analyze directly or …