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

• Autorzy: Przemysław Liszka
• 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.

Słowa kluczowe

EN

Lq spectra; Rényi dimension; Inhomogeneous self-similar measure; Homogeneous self-similar measure

Kategorie tematyczne

• 28A80: Fractals

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 9
• Strony: 1305-1319

Daty

wydano

2014-09-01

online

2014-05-08

Twórcy

autor

Przemysław Liszka

• University of Silesia

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Identyfikatory

DOI

10.2478/s11533-014-0414-1