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On circle rotations and the shrinking target properties

Jimmy Tseng
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Abstract

We generalize the monotone shrinking target property (MSTP) to the s-exponent monotone shrinking target property (sMSTP) and give a necessary and sufficient condition for a circle rotation to have sMSTP. Using another variant of MSTP, we obtain a new, very short, proof of a known result, which concerns the behavior of irrational rotations and implies a logarithm law similar to D. Sullivan's logarithm law for geodesics.

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Jimmy Tseng. 2007-10-09. On circle rotations and the shrinking target properties. https://arxiv.org/abs/math/0702853

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