Regular and Chaotic Dynamics

, Volume 16, Issue 1–2, pp 79–89 | Cite as

New directions in algebraic dynamical systems

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Abstract

The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.

Keywords

Dimer matchings domino tilings Mahler measure algebraic dynamics homoclinic points 

MSC2010 numbers

37A35 28D20 31C05 60J45 82B05 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of ViennaViennaAustria
  2. 2.Erwin Schrödinger Institute for Mathematical PhysicsViennaAustria
  3. 3.Mathematical InstituteUniversity of LeidenLeidenThe Netherlands
  4. 4.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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