Generalized fractal dimensions: equivalences and basic properties

[1]  L. Young.  Dimension, entropy and Lyapunov exponents , 1982, Ergodic Theory and Dynamical Systems.

[2]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[3]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[4]  Jensen,et al.  Erratum: Fractal measures and their singularities: The characterization of strange sets , 1986, Physical review. A, General physics.

[5]  I. Guarneri.  Spectral Properties of Quantum Diffusion on Discrete Lattices , 1989 .

[6]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[7]  C. D. Cutler.  Some results on the behavior and estimation of the fractal dimensions of distributions on attractors , 1991 .

[8]  K. Lau.  Fractal measures and mean p-variations , 1992 .

[9]  J. Combes.  Connections Between Quantum Dynamics and Spectral Properties of Time-Evolution Operators , 1993 .

[10]  S. Taylor,et al.  Fractal properties of products and projections of measures in ℝd , 1994, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  H. Weiss,et al.  On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and the Eckmann-Ruelle Conjecture , 1996 .

[12]  L. Olsen,et al.  A Multifractal Formalism , 1995 .

[13]  I. Guarneri.  Singular continuous spectra and discrete wave packet dynamics , 1996 .

[14]  M. Guysinsky,et al.  Coincidence of various dimensions associated with metrics and measures on metric spaces , 1997 .

[15]  H. Weiss,et al.  A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions , 1997 .

[16]  Y. Pesin.  Dimension Theory in Dynamical Systems: Contemporary Views and Applications , 1997 .

[17]  Anomalous Transport: A Mathematical Framework , 1997, cond-mat/9706239.

[18]  H. Weiss,et al.  The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples. , 1997, Chaos.

[19]  Remarks on the Relation between Quantum Dynamics and Fractal Spectra , 1997 .

[20]  K. Falconer.  Techniques in fractal geometry , 1997 .

[21]  Y. Heurteaux.  Estimations de la dimension infrieure et de la dimension suprieure des mesures , 1998 .

[22]  I. Guarneri,et al.  Intermittent Lower Bound on Quantum Diffusion , 1999 .

[23]  F. Takens,et al.  Multifractal Analysis of Local Entropies for Expansive Homeomorphisms with Specification , 1999 .

[24]  Yakov Pesin,et al.  Dimension and product structure of hyperbolic measures , 1999 .

[25]  F. Germinet,et al.  Nonlinear variation of diffusion exponents in quantum dynamics , 2000 .

[26]  Hermann Schulz-Baldes,et al.  Subdiffusive Quantum Transport for 3D Hamiltonians with Absolutely Continuous Spectra , 2000 .

[27]  L. Olsen.  Dimension inequalities of multifractal Hausdorff measures and multifractal packing measures , 2000 .

[28]  J. Combes,et al.  Fractal Dimensions and Quantum Evolution Associated with Sparse Potential Jacobi Matrices , 2001 .

[29]  FRACTAL DIMENSIONS AND THE PHENOMENON OF INTERMITTENCY IN QUANTUM DYNAMICS , 2001 .

[30]  I. Guarneri,et al.  Lower bounds on wave packet propagation by packing dimensions of spectral measures , 2002 .