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

Przemysław Liszka

Open Mathematics (2014)

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

Abstract

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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.

How to cite

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Przemysław 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 -

References

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