Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

DOI10.1063/1.4919767zbMath1374.37112OpenAlexW1867384304WikidataQ46436149 ScholiaQ46436149MaRDI QIDQ4591666

Igor Mezić, Zoran Levnajić

Publication date: 17 November 2017

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4919767

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items

Discrete chaotic maps obtained by symmetric integration, Modern Koopman Theory for Dynamical Systems, Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays, On the Approximation of Koopman Spectra for Measure Preserving Transformations, Application based construction and optimization of substitution boxes over 2D mixed chaotic maps, Unpredictability in Hamiltonian systems with a hierarchical phase space

Cites Work

• Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows
• The measure of chaos by the numerical analysis of the fundamental frequencies. Applications to the standard mapping
• Time-frequency analysis of chaotic systems
• Foundations of time-frequency analysis
• Comparison of systems with complex behavior
• Greene's residue criterion for the breakup of invariant tori of volume-preserving maps
• Spectral properties of dynamical systems, model reduction and decompositions
• On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
• Applied Koopmanism
• ADAPTIVE DATA ANALYSIS VIA SPARSE TIME-FREQUENCY REPRESENTATION
• Ergodic theory and experimental visualization of invariant sets in chaotically advected flows
• Symplectic maps, variational principles, and transport
• The Helical Transform as a Connection between Ergodic Theory and Harmonic Analysis
• On the Approximation of Complicated Dynamical Behavior
• Control of mixing in fluid flow: a maximum entropy approach
• A method for visualization of invariant sets of dynamical systems based on the ergodic partition
• Ergodic theory of chaos and strange attractors
• Average exit time for volume-preserving maps
• Self-organization in trees and motifs of two-dimensional chaotic maps with time delay
• Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets
• A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS
• Large deviations in non-uniformly hyperbolic dynamical systems
• Computing Invariant Manifolds by Integrating Fat Trajectories
• Break-up of invariant surfaces in action-angle-angle maps and flows
• Unnamed Item
• Unnamed Item
• Unnamed Item