Generalized Coupled Fibonacci Sequences

Rathore, G. P. S.; Jain, Shweta; Sikhwal, Omprakash

doi:10.5120/9567-4037

Cited by 2 publications

(1 citation statement)

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“…Coupled Fibonacci sequences have been considered in the literature, for instance in [59][60][61]. However, in these papers the possible applications to Hamiltonian dynamics, were not the topic of interest and moreover the corresponding maps were not symplectic.…”

Section: )mentioning

confidence: 99%

Arnol'd cat map lattices

Axenides¹,

Floratos²,

Nicolis³

2022

Preprint

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We construct Arnol'd cat map lattice field theories (ACML) with linear symplectic interactions, of tuneable locality in one or higher dimensions. The construction is based on the determination of special couplings for a system of n maps, the dynamics of each of which is described by a k−Fibonacci sequence.They provide examples of lattice field theories for interacting many-body deterministically chaotic oscillators.We study the classical spatio-temporal chaotic properties of these systems by using standard benchmarks for probing deterministic chaos of dynamical systems, namely the complete dense set of unstable periodic orbits, which, for long periods, lead to ergodicity and mixing.In the case of closed chains, with translational invariant couplings of tuneable locality, we find explicitly the spatiotemporal Lyapunov spectra as well as the Kolmogorov-Sinai entropy, as functions of the strength and the range of the interactions. The Kolmogorov-Sinai entropy is found to scale as the volume of the system.We provide methods to determine the spectrum of the periods of the unstable periodic orbits of the dynamical system and we observe that it exhibits a strong dependence on the strength and the range of the interaction.

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Section: )mentioning

confidence: 99%