Numerical analysis for a discontinuous rotation of the torus

H. Bruin; A. Lambert; G. Poggiaspalla; S. Vaienti

doi:10.1063/1.1572411

Numerical analysis for a discontinuous rotation of the torus

H. Bruin, A. Lambert, G. Poggiaspalla, S. Vaienti

Faculty of Science and Engineering

Research output: Contribution to journal › Article › Academic › peer-review

14 Citations (Scopus)

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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).

Original language	English
Pages (from-to)	558-571
Number of pages	14
Journal	Chaos
Volume	13
Issue number	2
DOIs	https://doi.org/10.1063/1.1572411
Publication status	Published - Jun-2003

Keywords

ROUND-OFF ERRORS
PIECEWISE ISOMETRIES
TOPOLOGICAL-ENTROPY
POLYGONAL BILLIARDS
DYNAMICS
MAPS

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Numerical analysis for a discontinuous rotation of the torusFinal publisher's version, 1.08 MBLicence: Unspecified

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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). ",

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AU - Bruin, H.

AU - Lambert, A.

AU - Poggiaspalla, G.

AU - Vaienti, S.

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N2 - 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).

AB - 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).

KW - ROUND-OFF ERRORS

KW - PIECEWISE ISOMETRIES

KW - TOPOLOGICAL-ENTROPY

KW - POLYGONAL BILLIARDS

KW - DYNAMICS

KW - MAPS

U2 - 10.1063/1.1572411

DO - 10.1063/1.1572411

M3 - Article

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VL - 13

SP - 558

EP - 571

JO - Chaos

JF - Chaos

IS - 2

ER -

Numerical analysis for a discontinuous rotation of the torus

Abstract

Keywords

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