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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 $ℤ^{d}$ -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.

Rigidity properties of $ℤ^{d}$ -actions on tori and solenoids.

Einsiedler, Manfred; Lindenstrauss, Elon — 2003

Electronic Research Announcements of the American Mathematical Society [electronic only]

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

Rigidity properties of ℤ d -actions on tori and solenoids.

Rigidity properties of $ℤ^{d}$ -actions on tori and solenoids.