On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions
From MaRDI portal
Publication:1279110
DOI10.1007/BF01058436zbMath0916.28006MaRDI QIDQ1279110
Publication date: 14 July 1999
Published in: Journal of Statistical Physics (Search for Journal in Brave)
Measure-preserving transformations (28D05) Fractals (28A80) Ergodic theory (37A99) Hausdorff and packing measures (28A78)
Related Items
Functional nonparametric model for time series: a fractal approach for dimension reduction, Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behavior, Wrinkling and fractalization of curves in an interface model of diffusionally unstable flames, The correlation dimension of the Sierpinski carpet, Bootstrap confidence intervals in functional nonparametric regression under dependence, Remark on metric analysis of reconstructed dynamics from chaotic time series, A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures, Correlation integral and determinism for a family of \(2^\infty\) maps, Remarks on the relation between quantum dynamics and fractal spectra, Mean of the singularities of a Gibbs measure, (Non)Invariance of dynamical quantities for orbit equivalent flows, Dimension and dimensional reduction in quantum gravity, Nonparametric recursive method for generalized kernel estimators for dependent functional data, Correlation dimension for iterated function systems, Formulas for complexity, invariant measure and RQA characteristics of the period-doubling subshift, Local Intrinsic Dimension Estimation by Generalized Linear Modeling, Fractal Dimensions and Random Transformations, Random Self-Similar Multifractals, Recurrence determinism and Li–Yorke chaos for interval maps, Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent, A note on the generalized fractal dimensions of a probability measure, The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples, Recursive nonparametric regression estimation for dependent strong mixing functional data, Fractals as objects with nontrivial structures at all scales, Local correlation entropy, Non-smooth saddle-node bifurcations II: Dimensions of strange attractors, Time-dependent scattering on fractal measures, Statistical decomposition of chaotic attractors by the eigenvectors of Oseledec matrix -- Active and passive information dynamics, Nearest neighbour distance and dimension of intensity measure of Poisson point process, Uniform lower bounds on the dimension of Bernoulli convolutions, Corrigendum to D. Simpelaere: Multifractal decomposition of the Sierpinski carpet., A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions, Ergodic theorems arising in correlation dimension estimation., On equivalent definitions of the correlation dimension for a probability measure, Stationary nonequilibrium states in boundary-driven Hamiltonian systems: Shear flow, Anomalous Transport: A Mathematical Framework, Unnamed Item, STRONG LAWS FOR RECURRENCE QUANTIFICATION ANALYSIS
Cites Work
- The Lyapunov dimension of strange attractors
- Connecting ergodicity and dimension in dynamical systems
- Dimension, entropy and Lyapunov exponents
- Dimension of invariant measures for maps with exponent zero
- Ergodic theory of chaos and strange attractors
- Dimension type characteristics for invariant sets of dynamical systems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
