Quantum arithmetic dynamics

Abstract

We study dynamics of the Lattès 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 Lattès maps can be reduced to the dynamics of the subshifts of finite type. Using such a reduction, we calculate the zeta function of the Lattès maps.

10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1503.05411