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Dynamical Systems
An International Journal
Volume 22, 2007 - Issue 1: Special issue on geometric dynamics with singularities, Guest editors: Arek Goetz–Sebastian van Strien–Franco Vivaldi
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Original Articles

Density of invariant disk packings for planar piecewise isometries

Rong-Zhong Yu College of Sciences, Jiujiang University, Jiujiang 332005, P.R. China
,
Xin-Chu Fu Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P.R. ChinaCorrespondence[email protected]
&
Shu-Liang Shui Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P.R. China; Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
Pages 65-72 | Received 18 Apr 2006, Accepted 22 Sep 2006, Published online: 06 Mar 2007
 
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Abstract

Iteration of a planar piecewise isometry may generate an invariant disk packing, and understanding the properties of the disk packing is helpful for estimating the Lebesgue measure of the exceptional set for the planar piecewise isometry. If the disk packing is not dense, then the Lebesgue measure of the exceptional set is positive. But it is not easy to check the density of a disk packing. In this paper, the authors present necessary and sufficient conditions for the density of a general disk packing, and discuss some properties of disk packings for planar piecewise isometries.

Acknowledgements

This research was supported jointly by NSFC Grant 10471087 and SRF for ROCS, SEM. Yu is also grateful to Jiujiang University for support via the university grant 06KJ28.

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