Exponential mixing of all orders for Arnol'd cat map lattices
| Autor: | Axenides, Minos, Floratos, Emmanuel, Nicolis, Stam |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 21 pages LaTeX, uses utphys.bst for bibliography style. v2: Typos and equation layout corrected. v3: References added and clarifying remarks in sections 2 and 6 |
| Databáze: | arXiv |
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