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arXiv · 1811.00299

Quantization dimension for infinite conformal iterated function systems

Jason Atnip·Mrinal Kanti Roychowdhury·Mariusz Urbański
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Abstract

The quantization dimension function for an $F$-conformal measure $m_F$ generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable H\"{o}lder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform the multifractal analysis, in our context of the measure $m_F$. The result in this paper extends a similar result of Lindsay and Mauldin established for finite conformal iterated function systems [Nonlinearity 15 (2002)].

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Jason Atnip, Mrinal Kanti Roychowdhury, Mariusz Urbański. 2018-11-01. Quantization dimension for infinite conformal iterated function systems. https://arxiv.org/abs/1811.00299

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