On a dimension of measures

• Autorzy: Lasota A. , Myjak J.
• Języki publikacji: EN

Abstrakty

EN

Using the notion of the Levy concentration function we discuss a definition of the dimension for probability measures. This dimension is strongly connected with the correlation dimension of measures and with the Hausdorff dimension of sets. Moreover, we calculate some bounds of this dimension for measures generated by Iterated Function Systems and by a partial differential equation.

Słowa kluczowe

EN

concentration dimension; fractals; Hausdorff dimension; invariant measures; iterated function systems; Levy concentration function; semifractals

PL

fraktal; miara niezmiennicza; układ funkcji iterowanej; wymiar Hausdorffa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 2
• Strony: 221--235
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Lasota A.

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
• Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40-013 Katowice, Poland

autor

Myjak J.

• Dipartimento di Matematica Pura Applicata, Universita di L’aquila, Via Vetoio, 67100 L’aquila, Italy

Bibliografia

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• [3] W. Hengartner, R. Theodorescu, Concentration functions, Academic Press, New York London 1973.
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• [6] A. Lasota, J. Myjak, Fractals, semifractals and Markov operators, Int. J. of Bifurcation and Chaos, 9 (1999) 307-325.
• [7] P. Lévy, Théorie de L’addition des Variables Aléatoires, Gautier-Villar, Paris 1937.
• [8] P. Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Univ. Press, Cambridge 1995.
• [9] E. Ott, Chaos in dynamical systems, Cambridge Univ. Press, Cambridge 1993.
• [10] R. Rudnicki, Invariant measures for the flow of a first order partial differential equation, Ergodic Theory Dynam. Systems, 5 (1985) 437-443.