Discretization of the Frobenius–Perron Operator Using a Sparse Haar Tensor Basis: The Sparse Ulam Method

DOI10.1137/080716864zbMath1210.37061arXiv0802.4006OpenAlexW2039587162MaRDI QIDQ3056237

Péter Koltai, Oliver Junge

Publication date: 11 November 2010

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.4006

zbMATH Keywords

sparse gridsUlam's methodPerron Frobenius operator

Mathematics Subject Classification ID

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Numerical problems in dynamical systems (65P99)

Related Items (15)

On the numerical approximation of the Perron-Frobenius and Koopman operator ⋮ Pseudogenerators of Spatial Transfer Operators ⋮ Improved approximation of phase-space densities on triangulated domains using discrete flow mapping with \(p\)-refinement ⋮ Sparsity enabled cluster reduced-order models for control ⋮ A boundary integral formalism for stochastic ray tracing in billiards ⋮ Perron–Frobenius Operator Filter for Stochastic Dynamical Systems ⋮ Learning to Forecast Dynamical Systems from Streaming Data ⋮ Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems ⋮ Transport of phase space densities through tetrahedral meshes using discrete flow mapping ⋮ Kernel embedding based variational approach for low-dimensional approximation of dynamical systems ⋮ Transition manifolds of complex metastable systems. Theory and data-driven computation of effective dynamics ⋮ Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis ⋮ Data-driven model reduction and transfer operator approximation ⋮ A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures ⋮ A Direction Preserving Discretization for Computing Phase-Space Densities

Uses Software

• GAIO

This page was built for publication: Discretization of the Frobenius–Perron Operator Using a Sparse Haar Tensor Basis: The Sparse Ulam Method