Quantum arithmetic dynamics
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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