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Density of invariant disk packings for planar piecewise isometries. (English) Zbl 1115.37045
Summary: 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.
37E30Homeomorphisms and diffeomorphisms of planes and surfaces
37B10Symbolic dynamics
37B40Topological entropy