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Quasiperiodic graphs at the onset of chaos
Luque Serrano, Bartolome and Cordero Gracia, Marta Amalia and Robledo, Alberto and Gómez López, Mariola
Quasiperiodic graphs at the onset of chaos.
"PHYSICAL REVIEW E", v. 88
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV)
algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos.
The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases
with the size of the network. We determine families of Pesin-like identities between entropy growth rates and
generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued
fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers
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