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A generalisation of Mahler measure and its application in algebraic dynamical systems

Manfred Einsiedler (1999)

Acta Arithmetica

We prove a generalisation of the entropy formula for certain algebraic d -actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.

A locally commutative free group acting on the plane

Kenzi Satô (2003)

Fundamenta Mathematicae

The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.

Analytic nonregular cocycles over irrational rotations

Mariusz Lemańczyk (1995)

Commentationes Mathematicae Universitatis Carolinae

Analytic cocycles of type I I I 0 over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.

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