Quasiperiodic graphs at the onset of chaos.
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.
Departamento Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Spain.
B
B
Luque
Departamento Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Spain.
M
M
Cordero-Gracia
Departamento Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Spain.
M
M
Gómez
Instituto de Física y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México, DF, Mexico.
A
A
Robledo