On circle rotations and the shrinking target properties

Details On circle rotations and the shrinking target properties On circle rotations and the shrinking target properties

2007-02-27

arxiv.org/abs/math/0702853v2

Mathematics

Dynamical Systems

13 pages. A new section has been added. The rest of the paper remains the same except for some very minor revisions.

Scientific paper

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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