Upper Estimate of Concentration and Thin Dimensions of Measures

Tom 57 / 2009

H. Gacki, A. Lasota, J. Myjak Bulletin Polish Acad. Sci. Math. 57 (2009), 149-162 MSC: Primary 37C45; Secondary 28A80, 11K55, 37C40. DOI: 10.4064/ba57-2-8

Streszczenie

We show upper estimates of the concentration and thin dimensions of measures invariant with respect to families of transformations. These estimates are proved under the assumption that the transformations have a squeezing property which is more general than the Lipschitz condition. These results are in the spirit of a paper by A. Lasota and J. Traple [Chaos Solitons Fractals 28 (2006)] and generalize the classical Moran formula.

Autorzy

  • H. GackiInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • A. Lasota[deceased]
  • J. MyjakDipartimento di Matematica Pura ed Applicata
    Università di L'Aquila
    Via Vetoio
    67100 L'Aquila, Italy
    and
    WMS AGH
    Al. Mickiewicza 30
    30-059 Kraków, Poland
    e-mail

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