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

Authors
Einsiedler, M
Citation
M. Einsiedler, A generalisation of Mahler measure and its application in algebraic dynamical systems, ACT ARITH, 88(1), 1999, pp. 15-29
Citations number
4
Categorie Soggetti
Mathematics
Journal title
ACTA ARITHMETICA
ISSN journal
00651036 → ACNP
Volume
88
Issue
1
Year of publication
1999
Pages
15 - 29
Database
ISI
SICI code
0065-1036(1999)88:1<15:AGOMMA>2.0.ZU;2-N
Abstract
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 lo garithm of the Mahler measure of a Laurent polynomial in d variables with i ntegral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system .