Distribution of periodic points of certain Gauss shifts with infinite invariant measure

On Invariant Möbius Measure and Gauss - Kuzmin Face Distribution

Consider an n-dimensional real vector space with lattice of integer points in it. The boundary of the convex hull of all integer points contained inside one of the n-dimensional invariant cones for a hyperbolic n-dimensional linear operator without multiple eigenvalues is called a sail in the sense of Klein. The set of all sails of such n-dimensional operator is called (n−1)-dimensional continu...

On recurrence equations associated with invariant varieties of periodic points

A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. Some of them had been known for some years, while some others have been found recently. In this contribution we would like to show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic points of higher dimensional integra...

Asymptotic Distribution of Divergence Measure with Applications

Invariant measure for an infinite neural network

A Family of Markov Shifts (almost) Classified by Periodic Points

Let G be a finite group, and let XG = {x = (x(s,t)) ∈ GZ 2 | x(s,t) = x(s,t−1) · x(s+1,t−1) for all (s, t) ∈ Z}. The compact zero–dimensional set XG carries a natural shift Z2–action σG and the pair ΣG = ( XG, σ G ) is a two–dimensional topological Markov shift. Using recent work by Crandall, Dilcher and Pomerance on the Fermat quotient, we show the following: if G is abelian, and the order of ...