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A NATURAL BOUNDARY FOR THE DYNAMICAL ZETA FUNCTION FOR COMMUTING GROUP AUTOMORPHISMS
"... Abstract. For an action α of Z d by homeomorphisms of a compact metric space, D. Lind introduced a dynamical zeta function and conjectured that this function has a natural boundary at the circle of convergence for d � 2. In this note, under the assumption that α is a mixing action by continuous auto ..."
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Abstract. For an action α of Z d by homeomorphisms of a compact metric space, D. Lind introduced a dynamical zeta function and conjectured that this function has a natural boundary at the circle of convergence for d � 2. In this note, under the assumption that α is a mixing action by continuous automorphisms of a compact connected abelian group of finite topological dimension, the unit circle is shown to be a natural boundary for this dynamical zeta function. 1.