Coherent structures and isolated spectrum for Perron–Frobenius cocycles

DOI10.1017/S0143385709000339zbMath1205.37015arXiv0804.1426WikidataQ59139583 ScholiaQ59139583MaRDI QIDQ3569985

Gary Froyland, Simon Lloyd, Anthony N. Quas

Publication date: 22 June 2010

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1426

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving maps of the interval (37E05)

Related Items (49)

Stability of hyperbolic Oseledets splittings for quasi-compact operator cocycles ⋮ 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 ⋮ Local stable and unstable manifolds and their control in nonautonomous finite-time flows ⋮ A spectral approach for quenched limit theorems for random expanding dynamical systems ⋮ A semi-invertible operator Oseledets theorem ⋮ Continuity of spectral radius over hyperbolic systems ⋮ Margulis–Ruelle inequality for general manifolds ⋮ Lyapunov exponents for transfer operator cocycles of metastable maps: A quarantine approach ⋮ On the periodic approximation of Lyapunov exponents for semi-invertible cocycles ⋮ Regularity of characteristic exponents and linear response for transfer operator cocycles ⋮ A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory ⋮ Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations ⋮ Dimension of invariant measures for affine iterated function systems ⋮ Study of hyperbolic measures for meromorphic maps ⋮ A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data ⋮ Characterization of dominated splittings for operator cocycles acting on Banach spaces ⋮ On the linearization of infinite‐dimensional random dynamical systems ⋮ A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems ⋮ Learning Theory for Dynamical Systems ⋮ Horseshoes and Lyapunov exponents for Banach cocycles over non-uniformly hyperbolic systems ⋮ Perturbation theory for the approximation of stability spectra by QR methods for sequences of linear operators on a Hilbert space ⋮ Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces ⋮ Weakly Birkhoff recurrent switching signals, almost sure and partial stability of linear switched dynamical systems ⋮ Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study ⋮ An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems ⋮ Periodic approximation of Oseledets subspaces for semi-invertible cocycles ⋮ Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles ⋮ Non-conformal repellers and the continuity of pressure for matrix cocycles ⋮ The generalised Berger-Wang formula and the spectral radius of linear cocycles ⋮ A Gel'fand-type spectral radius formula and stability of linear constrained switching systems ⋮ A concise proof of the multiplicative ergodic theorem on Banach spaces ⋮ Computing covariant Lyapunov vectors in Hilbert spaces ⋮ Understanding the geometry of transport: Diffusion maps for Lagrangian trajectory data unravel coherent sets ⋮ Hölder continuity of Oseledets splittings for semi-invertible operator cocycles ⋮ The metric entropy of random dynamical systems in a Banach space: Ruelle inequality ⋮ Finite-time entropy: a probabilistic approach for measuring nonlinear stretching ⋮ Pseudo-random endomorphisms in projective spaces. II ⋮ A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds ⋮ Hilbert space Lyapunov exponent stability ⋮ Explicit bounds for separation between Oseledets subspaces ⋮ Asymptotics for the second-largest Lyapunov exponent for some Perron–Frobenius operator cocycles ⋮ Multiplicative ergodic theorems for transfer operators: Towards the identification and analysis of coherent structures in non-autonomous dynamical systems ⋮ A remark on the invertibility of semi-invertible cocycles ⋮ Dimension estimates for non-conformal repellers and continuity of sub-additive topological pressure ⋮ Transport in time-dependent dynamical systems: Finite-time coherent sets ⋮ METASTABILITY, LYAPUNOV EXPONENTS, ESCAPE RATES, AND TOPOLOGICAL ENTROPY IN RANDOM DYNAMICAL SYSTEMS ⋮ Continuity of sub-additive topological pressure with matrix cocycles ^* ⋮ A semi-continuity theorem for the entropy of meromorphic maps

Cites Work

• Unnamed Item
• Strange eigenmodes and decay of variance in the mixing of diffusive tracers
• The thermodynamic formalism for expanding maps
• Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps
• On the concept of stationary Lyapunov basis
• On the rate of convergence to equilibrium in one-dimensional systems
• Ergodic properties of invariant measures for piecewise monotonic transformations
• Statistically optimal almost-invariant sets
• Lagrangian coherent structures and mixing in two-dimensional turbulence
• On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps
• Lyapunov exponents for continuous transformations and dimension theory
• Banach spaces adapted to Anosov systems
• A Dynamical Proof of the Multiplicative Ergodic Theorem
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Random perturbations of chaotic dynamical systems: stability of the spectrum
• On the Approximation of Complicated Dynamical Behavior
• On the isolated spectrum of the Perron-Frobenius operator
• Eigenfunctions for smooth expanding circle maps
• Ruelle Perron Frobenius spectrum for Anosov maps
• TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS
• Distinguished material surfaces and coherent structures in three-dimensional fluid flows

This page was built for publication: Coherent structures and isolated spectrum for Perron–Frobenius cocycles