Abstract
AbstractVery 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.
Reference25 articles.
1. Arbeiter M., Patzschke N., Random self-similar multifractals, Math. Nachr., 1996, 181, 5–42
2. Cambridge Nonlinear Sci. Ser.;R Badii,1997
3. Bárány B., On the Hausdorff dimension of a family of self-similar sets with complicated overlaps, Fund. Math., 2009, 206, 49–59
4. Barnsley M.F., Fractals Everywhere, 2nd ed., Academic Press, Boston, 1993
5. Barnsley M.F., Superfractals, Cambridge University Press, Cambridge, 2006
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献