Riddling and invariance for discontinuous maps preserving Lebesgue measure

Ashwin, Peter, Fu, Xin-Chu and Terry, John R. (2002) Riddling and invariance for discontinuous maps preserving Lebesgue measure. Nonlinearity, 15 3: 633-645. doi:10.1088/0951-7715/15/3/306

Author Ashwin, Peter
Fu, Xin-Chu
Terry, John R.
Title Riddling and invariance for discontinuous maps preserving Lebesgue measure
Journal name Nonlinearity   Check publisher's open access policy
ISSN 0951-7715
Publication date 2002-05
Sub-type Article (original research)
DOI 10.1088/0951-7715/15/3/306
Volume 15
Issue 3
Start page 633
End page 645
Total pages 13
Place of publication United Kingdom
Publisher Institute of Physics Publishing
Collection year 2002
Language eng
Subject C1
780101 Mathematical sciences
0102 Applied Mathematics
Abstract In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.
Keyword Mathematics, Applied
Physics, Mathematical
Digital-filter Overflow
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 19 times in Thomson Reuters Web of Science Article | Citations
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Created: Tue, 14 Aug 2007, 17:03:41 EST