Numerical analysis for a discontinuous rotation of the torus

Chaos
H BruinS Vaienti

Abstract

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).

References

Jan 1, 1987·Physical Review A: General Physics·K Pawelzik, H G Schuster
Nov 1, 1987·Physical Review A: General Physics·K Pawelzik, H G Schuster
Jun 5, 2003·Chaos·J. H. Lowenstein, F. Vivaldi

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Citations

Apr 20, 2019·Physical Review. E·Thomas F LynnRichard M Lueptow
Nov 17, 2020·Research in Number Theory·Paul Surer

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