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

• Autorzy: Manfred Einsiedler
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28D15: General groups of measure-preserving transformations
• 11R04: Algebraic numbers; rings of algebraic integers
• 28D20: Entropy and other invariants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 88
• Numer: 1
• Strony: 15-29

Daty

wydano

1999

otrzymano

1997-09-08

poprawiono

1998-09-21

Twórcy

autor

Manfred Einsiedler

• Mathematical Institute, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria

Bibliografia

• [1] D. Hilbert, Gesammelte Abhandlungen, Bd. I, Springer, Berlin, 1932.
• [2] D. A. Lind, K. Schmidt and T. Ward, Mahler measure and entropy for commuting automorphisms of compact groups, Invent. Math. 101 (1990), 593-629.
• [3] J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1992.
• [4] K. Schmidt, Dynamical Systems of Algebraic Origin, Birkhäuser, 1995.