dc.contributor.author | Trovati, Marcello | |
dc.contributor.author | Ashwin, Peter | |
dc.contributor.author | Byott, Nigel P. | |
dc.date.accessioned | 2013-04-19T15:46:36Z | |
dc.date.issued | 2008-09-01 | |
dc.description.abstract | Planar piecewise isometries with convex polygonal atoms that are piecewise irrational rotations can naturally generate a packing of phase space given by periodic cells that are discs. We show that such packings cannot contain certain subpackings of Apollonian packings, namely those belonging to a family of Arbelos subpackings. We do this by showing that the unit complex numbers giving the directions of tangency within such an isometric-generated packing lie in a finitely generated subgroup of the circle group, whereas this is not the case for the Arbelos subpackings. In the opposite direction, we show that, given an arbitrary disc packing of a polygonal region, there is a piecewise isometry whose regular cells approximate the given packing to any specified precision. | en_GB |
dc.identifier.citation | Vol. 22 (3), pp. 791 - 806 | en_GB |
dc.identifier.doi | 10.3934/dcds.2008.22.791 | |
dc.identifier.uri | http://hdl.handle.net/10871/8383 | |
dc.language.iso | en | en_GB |
dc.publisher | American Institute of Mathematical Sciences (AIMS) | en_GB |
dc.subject | Piecewise isometries | en_GB |
dc.subject | apollonian circle packings | en_GB |
dc.title | Packings induced by piecewise isometries cannot contain the Arbelos | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2013-04-19T15:46:36Z | |
dc.identifier.issn | 1078-0947 | |
dc.description | Copyright © American Institute of Mathematical Sciences | en_GB |
dc.identifier.eissn | 1553-5231 | |
dc.identifier.journal | Discrete and Continuous Dynamical Systems - Series A | en_GB |