Quantum arithmetic dynamics

Igor Nikolaev

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arXiv · 2112.11297

Quantum arithmetic dynamics

Igor Nikolaev

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Abstract

We study dynamics of the Latt\`es maps in the complex plane in terms of the Cuntz-Krieger algebras associated to the endomorphisms of the non-commutative tori. In particular, it is shown that iterations of the Latt\`es maps can be reduced to the dynamics of the subshifts of finite type. Using such a reduction, we calculate the zeta function of the Latt\`es maps.

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Igor Nikolaev. 2021-12-21. Quantum arithmetic dynamics. https://arxiv.org/abs/2112.11297

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