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.
|Number of pages||12|
|Journal||Discrete and Continuous Dynamical Systems (DCDS-A)|
|Publication status||Published - Apr 2008|
- Circle rotations
- Continued fractions
- Diophantine approximation
- Logarithm laws