# Arnol'd cat map lattices

Abstract : 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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https://hal.archives-ouvertes.fr/hal-03747767
Contributor : Stam Nicolis Connect in order to contact the contributor
Submitted on : Monday, August 8, 2022 - 4:21:47 PM
Last modification on : Tuesday, August 9, 2022 - 3:28:15 AM

### Identifiers

• HAL Id : hal-03747767, version 1
• ARXIV : 2208.03267

### Citation

Minos Axenides, Emmanuel Floratos, Stam Nicolis. Arnol'd cat map lattices. 2022. ⟨hal-03747767⟩

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