101 research outputs found
Symmetry of entropy in higher rank diagonalizable actions and measure classification
An important consequence of the theory of entropy of Z-actions is that the
events measurable with respect to the far future coincide (modulo null sets)
with those measurable with respect to the distant past, and that measuring the
entropy using the past will give the same value as measuring it using the
future. In this paper we show that for measures invariant under multiparameter
algebraic actions if the entropy attached to coarse Lyapunov foliations fail to
display a stronger symmetry property of a similar type this forces the measure
to be invariant under non-trivial unipotent groups. Some consequences of this
phenomenon are noted
Periodic points for good reduction maps on curves
The periodic points of a morphism of good reduction for a smooth projective
curve with good reduction over the p-adics form a discrete set. This is used to
give an interpretation of the morphic height in terms of asymptotic properties
of periodic points, and a morphic analogue of Jensen's formula
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