Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps

DOI10.1016/j.physd.2007.11.004zbMath1157.37011OpenAlexW2140130898WikidataQ59139590 ScholiaQ59139590MaRDI QIDQ926804

Gary Froyland

Publication date: 21 May 2008

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2007.11.004

zbMATH Keywords

Perron-Frobenius operatoreigenfunctionsstandard mapdecay of correlationsUlam's methodhyperbolic mapeigendistributionalmost-invariant setsisolated spectrum

Mathematics Subject Classification ID

Smooth dynamical systems: general theory (37C99)

Related Items (10)

Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows ⋮ Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix Cocycles ⋮ A semi-invertible operator Oseledets theorem ⋮ Coherent structures and isolated spectrum for Perron–Frobenius cocycles ⋮ Finite-time entropy: a probabilistic approach for measuring nonlinear stretching ⋮ Coherent sets for nonautonomous dynamical systems ⋮ Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools ⋮ Data-driven spectral decomposition and forecasting of ergodic dynamical systems ⋮ Transport in time-dependent dynamical systems: Finite-time coherent sets ⋮ Eigenfunctions of the Perron–Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps

Uses Software

• GAIO

Cites Work

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• On the Approximation of Complicated Dynamical Behavior
• Estimating physical invariant measures and space averages of dynamical systems indicators
• On the isolated spectrum of the Perron-Frobenius operator
• Ruelle Perron Frobenius spectrum for Anosov maps
• Chaos

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