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dc.contributor.authorAshwin, Peteren_GB
dc.contributor.authorGoetz, Areken_GB
dc.contributor.departmentUniversity of Exeter; San Francisco State Universityen_GB
dc.date.accessioned2008-02-27T14:16:47Zen_GB
dc.date.accessioned2011-01-25T10:33:14Zen_GB
dc.date.accessioned2013-03-20T12:31:06Z
dc.date.issued2005en_GB
dc.description.abstractWe investigate a remarkable new planar piecewise isometry whose generating map is a permutation of four cones. For this system we prove the coexistence of an infinite number of periodic components and an uncountable number of transitive components. The union of all periodic components is an invariant pentagon with unequal sides. Transitive components are invariant curves on which the dynamics are conjugate to a transitive interval exchange. The restriction of the map to the invariant pentagonal region is the first known piecewise isometric system for which there exist an infinite number of periodic components but the only aperiodic points are on the boundary of the region. The proofs are based on exact calculations in a rational cyclotomic field. We use the system to shed some light on a conjecture that PWIs can possess transitive invariant curves that are not smooth.en_GB
dc.identifier.citation358 (1), pp. 373-390en_GB
dc.identifier.urihttp://hdl.handle.net/10036/19239en_GB
dc.language.isoenen_GB
dc.publisherAmerican Mathematical Societyen_GB
dc.relation.urlhttp://www.ams.org/tran/2006-358-01/S0002-9947-05-03670-6/home.htmlen_GB
dc.subjectpiecewise isometryen_GB
dc.subjectinterval exchange transformationen_GB
dc.subjectcellsen_GB
dc.titlePolygonal invariant curves for a planar piecewise isometryen_GB
dc.typeArticleen_GB
dc.date.available2008-02-27T14:16:47Zen_GB
dc.date.available2011-01-25T10:33:14Zen_GB
dc.date.available2013-03-20T12:31:06Z
dc.identifier.issn0002-9947en_GB
dc.descriptionCopyright © 2005 American Mathematical Society. First published in Transactions of the American Mathematical Society in Vol. 358 no. 1 (2005), published by the American Mathematical Society.en_GB
dc.identifier.journalTransactions of the American Mathematical Societyen_GB


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