Correlation dimension and phase space contraction via extreme value theory

DOI10.1063/1.5027386zbMath1390.37130arXiv1711.03021OpenAlexW3104646270WikidataQ57886082 ScholiaQ57886082MaRDI QIDQ4565964

Davide Faranda, Sandro Vaienti

Publication date: 13 June 2018

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

Full work available at URL: https://arxiv.org/abs/1711.03021

Mathematics Subject Classification ID

Simulation of dynamical systems (37M05) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (10)

A stream cipher algorithm based on 2D coupled map lattice and partitioned cellular automata ⋮ Dynamical systems approaches to the study of climate with applications to 2022 extreme weather events ⋮ On the shortest distance between orbits and the longest common substring problem ⋮ Extreme value distributions of observation recurrences ⋮ Generalized dimensions, large deviations and the distribution of rare events ⋮ Shortest distance between multiple orbits and generalized fractal dimensions ⋮ Network measures of mixing ⋮ On the computation of the extremal index for time series ⋮ Sampling hyperspheres via extreme value theory: implications for measuring attractor dimensions ⋮ Matching of observations of dynamical systems, with applications to sequence matching

Cites Work

• Unnamed Item
• Numerical convergence of the block-maxima approach to the generalized extreme value distribution
• Hausdorff dimensions in two-dimensional maps and thermodynamic formalism
• Hitting time statistics and extreme value theory
• Testing for nonlinearity in time series: the method of surrogate data
• Determining Lyapunov exponents from a time series
• Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
• Generalized dimensions, entropies, and Lyapunov exponents from the pressure function for strange sets.
• A practical method for calculating largest Lyapunov exponents from small data sets
• Rare events, escape rates and quasistationarity: Some Exact formulae
• Extreme value theory for singular measures
• Extremes and Recurrence in Dynamical Systems
• The problem of spurious Lyapunov exponents in time series analysis and its solution by covariant Lyapunov vectors
• Extreme value statistics for dynamical systems with noise
• Rare events, exponential hitting times and extremal indices via spectral perturbation†
• Escape rates for Gibbs measures
• Laws of rare events for deterministic and random dynamical systems
• The Hausdorff dimension of the Smale-Williams solenoid with different contraction coefficients
• Lyapunov Exponents
• Dimension, entropy and Lyapunov exponents
• THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS
• Nonlinear Time Series Analysis
• IMPROVED CORRELATION DIMENSION CALCULATION
• Lectures on Lyapunov Exponents

This page was built for publication: Correlation dimension and phase space contraction via extreme value theory