Geodesic
Upper Estimate of Concentration and Thin Dimensions of Measures
H. Gacki 1   ; A. Lasota 2   ; J. Myjak 3
1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
2 [deceased]
3 Dipartimento 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
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 149-162 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba57-2-8
Keywords: upper estimates concentration thin dimensions measures invariant respect families transformations these estimates proved under assumption transformations have squeezing property which general lipschitz condition these results spirit paper lasota traple chaos solitons fractals generalize classical moran formula

H. Gacki  1   ; A. Lasota  2   ; J. Myjak  3

1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
2 [deceased]
3 Dipartimento 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 
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     title = {Upper {Estimate} of {Concentration} and {Thin} {Dimensions} of {Measures}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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H. Gacki; A. Lasota; J. Myjak. Upper Estimate of Concentration and Thin Dimensions of Measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 149-162. doi: 10.4064/ba57-2-8

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