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

Open Mathematics (2014)

- Volume: 12, Issue: 9, page 1305-1319
- ISSN: 2391-5455

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topPrzemysław Liszka. "The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures." Open Mathematics 12.9 (2014): 1305-1319. <http://eudml.org/doc/269471>.

@article{PrzemysławLiszka2014,

abstract = {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.},

author = {Przemysław Liszka},

journal = {Open Mathematics},

keywords = {Lq spectra; Rényi dimension; Inhomogeneous self-similar measure; Homogeneous self-similar measure; spectra; inhomogeneous self-similar measure; homogeneous self-similar measure},

language = {eng},

number = {9},

pages = {1305-1319},

title = {The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures},

url = {http://eudml.org/doc/269471},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Przemysław Liszka

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

JO - Open Mathematics

PY - 2014

VL - 12

IS - 9

SP - 1305

EP - 1319

AB - 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.

LA - eng

KW - Lq spectra; Rényi dimension; Inhomogeneous self-similar measure; Homogeneous self-similar measure; spectra; inhomogeneous self-similar measure; homogeneous self-similar measure

UR - http://eudml.org/doc/269471

ER -

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