|
| next >> |
Journal description
All volumes of the corresponding journal
All issues of the corresponding volume
All articles of the corresponding issues
Details for article 1 of 6 found articles
| Title: |
Aperiodic orbits of piecewise rational rotations of convex polygons with recursive tiling |
| Author: |
Lowenstein, J. H. |
| Appeared in: |
Dynamical systems |
| Paging: | Volume 22 (2007) nr. 1 pages 25-63 |
| Year: |
2007-03 |
| Contents: |
We study piecewise rational rotations of convex polygons with a recursive tiling property. For these dynamical systems, the set Σ of discontinuity-avoiding aperiodic orbits decomposes into invariant subsets endowed with a hierarchical symbolic dynamics (Vershik map on a Bratteli diagram). Under conditions which guarantee a form of asymptotic temporal scaling, we prove minimality and unique ergodicity for each invariant component. We study the multi-fractal properties of the model with respect to recurrence times, deriving a method of successive approximations for the generalized dimensions α(q). We consider explicit examples in which the trace of the rotation matrix is a quadratic or cubic irrational, and evaluate numerically, with high precision, the function α(q) and its Legendre transform. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 1 of 6 found articles
| next >> |