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arXiv · 1505.02547

The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities

Vladimir Garcia-Morales
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Abstract

A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (generally fractal functions), the decomposition being both exact and valid everywhere on the domain of the function.

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BibTeXRIS

Vladimir Garcia-Morales. 2015-05-11. The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities. https://doi.org/10.1016/j.chaos.2015.11.028

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