| JEAN-PAUL THOUVENOT ∗∗ (2009) | |||||||||||||
Abstract | |||||||||||||
| Abstract. We define invariants for measure–preserving actions of discrete amenable groups which characterize various subexponential rates of growth for the number of “essential ” orbits similarly to the way entropy of the action characterizes the exponential growth rate. We obtain above estimates for these invariants or actions by diffeomorphisms of a compact manifold (with a Borel invariant measure) and, more generally, by Lipschitz homeomorphisms of a compact metric space of finite box dimension. We show that natural cutting and stacking constructions alternating independent and periodic concatenation of names produce Z 2 actions with zero onedimensional entropies in all (including irrational) directions which do not allow either of the above realizations. | |||||||||||||
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