Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
We propose a framework to define dimensions of Borel measures in a metric space by formulating a set of natural properties for a measure-dimension mapping, namely monotonicity, bi-Lipschitz invariance, (σ-)stability, etc. We study the behaviour of most popular definitions of measure dimensions in regard to our list, with special attention to the standard correlation dimensions and their modified versions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
219-233
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-02-04
poprawiono
1999-04-29
Twórcy
autor
- Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
autor
- Departamento de Análisis Económico, Universidad Complutense, Campus de Somosaguas, 28223 Madrid, Spain
autor
- Departamento de Análisis Económico, Universidad Complutense, Campus de Somosaguas, 28223 Madrid, Spain
Bibliografia
- [1] L. Barreira, Ya. Pesin and J. Schmeling, Dimensions of hyperbolic measures--a proof of the Eckmann-Ruelle conjecture, Ann. of Math., to appear.
- [2] C. D. Cutler, Some results on the behaviour and estimation of the fractal dimensions of distributions on attractors, J. Stat. Phys. 62 (1990), 651-708.
- [3] K. J. Falconer, Fractal Geometry--Mathematical Foundations and Applications, Wiley, 1990.
- [4] K. J. Falconer, Techniques in Fractal Geometry, Wiley, 1998.
- [5] P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50 (1983), 346-349.
- [6] M. de Guzmán, Differentiation of Integrals in $ℝ^n$, Lecture Notes in Math. 481, Springer, 1975.
- [7] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Univ. Press, 1995.
- [8] Ya. Pesin, On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions, J. Statist. Phys. 71 (1993), 529-547.
- [9] L.-S. Young, Dimension, entropy and Liapunov exponents, Ergodic Theory Dynam. Systems 2 (1982), 109-124.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv142i3p219bwm