Numerical analysis for a discontinuous rotation of the torus.
In this paper, we study a class of piecewise rotations on the square. While few theoretical results are known about them, we numerically compute box-counting dimensions, correlation dimensions and complexity of the symbolic language produced by the system. Our results seem to confirm a conjecture that the fractal dimension of the exceptional set is two, as well as indicate that the dynamics on it is not ergodic. We also explore a relationship between the piecewise rotations and discretized rotations on lattices Z(2n).
Bruin
H
H
Department of Mathematics, University of Groningen, Groningen, The Netherlands. bruin@math.rug.nl
Lambert
A
A
Poggiaspalla
G
G
Vaienti
S
S