Linearization in the large of nonlinear systems and Koopman operator spectrum
From MaRDI portal
Publication:1935169
DOI10.1016/j.physd.2012.08.017zbMath1260.34073OpenAlexW2069159682MaRDI QIDQ1935169
Publication date: 30 January 2013
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2012.08.017
Periodic solutions to ordinary differential equations (34C25) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Dynamical systems with hyperbolic orbits and sets (37D05) Nonlinear ordinary differential operators (34L30)
Related Items
Vibrational mono-/bi-resonance and wave propagation in FitzHhugh-Nagumo neural systems under electromagnetic induction, Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows, Modern Koopman Theory for Dynamical Systems, Global linearization and fiber bundle structure of invariant manifolds, Unnamed Item, Time-Delay Observables for Koopman: Theory and Applications, Physics-Informed Probabilistic Learning of Linear Embeddings of Nonlinear Dynamics with Guaranteed Stability, Data-driven feedback stabilisation of nonlinear systems: Koopman-based model predictive control, Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics, Spectral analysis of the Koopman operator for partial differential equations, Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems, Resonances in a chaotic attractor crisis of the Lorenz flow, Koopman operator spectrum for random dynamical systems, Spectrum of the Koopman operator, spectral expansions in functional spaces, and state-space geometry, Go with the flow, on Jupiter and snow. Coherence from model-free video data without trajectories, Geometric considerations of a good dictionary for Koopman analysis of dynamical systems: cardinality, ``primary eigenfunction, and efficient representation, Global computation of phase-amplitude reduction for limit-cycle dynamics, On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions, Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits, Koopman Resolvent: A Laplace-Domain Analysis of Nonlinear Autonomous Dynamical Systems, Sparsity Structures for Koopman and Perron--Frobenius Operators
Cites Work
- Geometry of the ergodic quotient reveals coherent structures in flows
- Local \(C^n\) transformations of the real line
- Hartman's linearization on nonautonomous unbounded system
- Strongly topological linearization with generalized exponential dichotomy
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Normal hyperbolicity and linearisability
- Topological equivalence of normally hyperbolic dynamical systems
- Asymptotic stability equals exponential stability, and ISS equals finite energy gain -- if you twist your eyes.
- The Lorenz equations: bifurcations, chaos, and strange attractors
- Comparison of systems with complex behavior
- On Hartman's linearization theorem and Palmer's linearization theorem
- A generalization of Hartman's linearization theorem
- Linearization of normally hyperbolic diffeomorphisms and flows
- On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
- Non-perturbative linearization of dynamical systems
- A method for visualization of invariant sets of dynamical systems based on the ergodic partition
- Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets
- A Lemma in the Theory of Structural Stability of Differential Equations
- On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations
- A new class of linearizable equations
- Global topological linearization in critical case
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item