Exponential mixing of all orders for Arnol'd cat map lattices

Minos Axenides; Emmanuel Floratos; Stam Nicolis

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arXiv · 2401.08521

Exponential mixing of all orders for Arnol'd cat map lattices

Minos Axenides·Emmanuel Floratos·Stam Nicolis

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Abstract

We show that the recently introduced classical Arnol'd cat map lattice field theories, which are chaotic, are exponentially mixing to all orders. Their mixing times are well-defined and are expressed in terms of the Lyapunov exponents, more precisely by the combination that defines the inverse of the Kolmogorov-Sinai entropy of these systems. We prove by an explicit recursive construction of correlation functions, that these exhibit $l-$fold mixing for any $l= 3,4,5,\ldots$. This computation is relevant for Rokhlin's conjecture, which states that 2-fold mixing induces $l-$fold mixing for any $l>2$. Our results show that 2-fold exponential mixing, while being necessary for any $l-$fold mixing to hold it is nevertheless not sufficient for Arnol'd cat map lattice field theories.

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Minos Axenides, Emmanuel Floratos, Stam Nicolis. 2024-01-16. Exponential mixing of all orders for Arnol'd cat map lattices. https://arxiv.org/abs/2401.08521

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