Quantum arithmetic dynamics
Operator Algebras
2021-12-22 v1 Dynamical Systems
Number Theory
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.
Cite
@article{arxiv.2112.11297,
title = {Quantum arithmetic dynamics},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:2112.11297},
year = {2021}
}
Comments
10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1503.05411