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arXiv · 1203.3717

Quasiperiodic graphs: structural design, scaling and entropic properties

Bartolo Luque·Fernando J. Ballesteros·Ángel M. Núñez·Alberto Robledo
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Abstract

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy.

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Bartolo Luque, Fernando J. Ballesteros, Ángel M. Núñez, Alberto Robledo. 2012-03-16. Quasiperiodic graphs: structural design, scaling and entropic properties. https://doi.org/10.1007/s00332-012-9153-2

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