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On circle rotations and the shrinking target properties
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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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Cited by 1 Pith paper
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Self-Referential Leading Digits of Exponential Sequences: Arithmetic Structure and Certified Search
Self-prefix hits of c^m admit exact discrepancy identities, Lambert two-gap candidates, resonance rigidity, and certified O(N^{1-1/ν} polylog N) search; infinitude of 2^m starting with m remains open.
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