Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools

DOI10.3934/jcd.2014.1.249zbMath1346.37066OpenAlexW2037558275MaRDI QIDQ2513917

Cecilia González-Tokman, Gary Froyland, Anthony N. Quas

Publication date: 29 January 2015

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jcd.2014.1.249

zbMATH Keywords

metastabilitytransfer operatorsUlam's methodKoopman operators

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (13)

A trajectory-free framework for analysing multiscale systems ⋮ Stability of hyperbolic Oseledets splittings for quasi-compact operator cocycles ⋮ Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix Cocycles ⋮ Modern Koopman Theory for Dynamical Systems ⋮ Dynamic mode decomposition for analytic maps ⋮ Fourier approximation of the statistical properties of Anosov maps on tori ⋮ Koopman operator framework for time series modeling and analysis ⋮ Reproducing kernel Hilbert space compactification of unitary evolution groups ⋮ Dynamic mode decomposition for continuous time systems with the Liouville operator ⋮ Delay-coordinate maps and the spectra of Koopman operators ⋮ Multiplicative ergodic theorems for transfer operators: Towards the identification and analysis of coherent structures in non-autonomous dynamical systems ⋮ Data-driven spectral decomposition and forecasting of ergodic dynamical systems ⋮ Estimating long-term behavior of periodically driven flows without trajectory integration

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