Rigorous computation of invariant measures and fractal dimension for maps with contracting fibers: 2D Lorenz-like maps

DOI10.1017/etds.2014.145zbMath1378.37048OpenAlexW2333253793MaRDI QIDQ2827500

Isaia Nisoli, Stefano Galatolo

Publication date: 20 October 2016

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

Full work available at URL: http://hdl.handle.net/11568/797616

zbMATH Keywords

invariant measureone-dimensional mapWasserstein distancecontracting foliation

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Dimension theory of smooth dynamical systems (37C45)

Related Items (13)

Rigorous approximation of diffusion coefficients for expanding maps ⋮ Chaotic itinerancy in random dynamical system related to associative memory models ⋮ Application of rotational spectrum for correlation dimension estimation ⋮ Fast Adjoint Algorithm for Linear Responses of Hyperbolic Chaos ⋮ Recursive divergence formulas for perturbing unstable transfer operators and physical measures ⋮ Backpropagation in hyperbolic chaos via adjoint shadowing ⋮ Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof ⋮ Tight space-noise tradeoffs in computing the ergodic measure ⋮ A rigorous computational approach to linear response ⋮ An elementary way to rigorously estimate convergence to equilibrium and escape rates ⋮ Automatic generation of bounds for polynomial systems with application to the Lorenz system ⋮ Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors ⋮ Locating Ruelle–Pollicott resonances*

Cites Work

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• Local dimension of ergodic measures for two-dimensional Lorenz transformations

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