Ergodic properties and KMS conditions on -symbolic dynamical systems
Kengo MatsumotoDepartment of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan
A -symbolic dynamical system consists of a unital -algebra and a finite family of endomorphisms of indexed by symbols of satisfying some conditions. The endomorphisms yield both a subshift and a -algebra . We will study ergodic properties of the positive operator on . We will next introduce KMS conditions for continuous linear functionals on under gauge action at inverse temperature taking its value in complex numbers. We will study relationships among the eigenvectors of in , the continuous linear functionals on satisfying KMS conditions and the invariant measures on the associated one-sided shifts. We will finally present several examples of continuous linear functionals satisfying KMS conditions.
Cite this article
Kengo Matsumoto, Ergodic properties and KMS conditions on -symbolic dynamical systems. Doc. Math. 16 (2011), pp. 133–175DOI 10.4171/DM/329