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Dlask, Martin; Kukal, Jaromir

Translation and rotation invariant method of Renyi dimension estimation. (English) Zbl 1415.65005

Chaos Solitons Fractals 114, 536-541 (2018).
Summary: A is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented, and for the analysis of , a novel approach that employs the log-linear dependence of a modified Renyi entropy is used. The new formula for the Renyi entropy has been investigated both theoretically and experimentally on selected .
© Elsevier Ltd

Cited in 1 Document

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
28D20 Entropy and other invariants
65C05 Monte Carlo methods

Keywords:

Parzen estimate; Renyi entropy; Monte Carlo; Renyi dimension
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References:

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