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2014 | 12 | 9 | 1305-1319

Tytuł artykułu

The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
Very recently bounds for the L q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and probabilities depending on positions. As an application of the results, we provide a systematic approach to obtaining non-trivial bounds for the L q spectra and Rényi dimension of inhomogeneous self-similar measures not satisfying the IOSC and of homogeneous ones not satisfying the OSC. We also provide some non-trivial bounds without any separation conditions.

Kategorie tematyczne

Wydawca

Czasopismo

Rocznik

Tom

12

Numer

9

Strony

1305-1319

Opis fizyczny

Daty

wydano
2014-09-01
online
2014-05-08

Twórcy

  • University of Silesia

Bibliografia

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  • [11] Feng D.-J., Olivier E., Multifractal analysis of weak Gibbs measures and phase transition - application to some Bernoulli convolutions, Ergodic Theory Dynam. Systems, 2003, 23(6), 1751–1784 http://dx.doi.org/10.1017/S0143385703000051
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  • [15] Lau K.-S., Self-similarity, L p-spectrum and multifractal formalism, In: Fractal Geometry and Stochastics, Progr. Probab., 37, Birkhäuser, Basel, 1995, 55–90 http://dx.doi.org/10.1007/978-3-0348-7755-8_4
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  • [17] Lau K.-S., Ngai S.-M., L q-spectrum of Bernoulli convolutions associated with P. V. numbers, Osaka J. Math., 1999, 36(4), 993–1010
  • [18] Liszka P., On inhomogeneous self-similar measures and their L q spectra, Ann. Polon. Math., 2013, 109(1), 75–92 http://dx.doi.org/10.4064/ap109-1-6
  • [19] Olsen L., Snigireva N., L q spectra and Rényi dimensions of in-homogeneous self-similar measures, Nonlinearity, 2007, 20(1), 151–175 http://dx.doi.org/10.1088/0951-7715/20/1/010
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Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_s11533-014-0414-1
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