Polygonal invariant curves for a planar piecewise isometry

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Polygonal invariant curves for a planar piecewise isometry

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Goetz, Arek en_GB
dc.contributor.department University of Exeter; San Francisco State University en_GB
dc.date.accessioned 2008-02-27T14:16:47Z en_GB
dc.date.accessioned 2011-01-25T10:33:14Z en_US
dc.date.accessioned 2013-03-20T12:31:06Z
dc.date.issued 2005 en_GB
dc.description.abstract We 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.citation 358 (1), pp. 373-390 en_GB
dc.identifier.uri http://hdl.handle.net/10036/19239 en_GB
dc.language.iso en en_GB
dc.publisher American Mathematical Society en_GB
dc.relation.url http://www.ams.org/tran/2006-358-01/S0002-9947-05-03670-6/home.html en_GB
dc.subject piecewise isometry en_GB
dc.subject interval exchange transformation en_GB
dc.subject cells en_GB
dc.title Polygonal invariant curves for a planar piecewise isometry en_GB
dc.type Article en_GB
dc.date.available 2008-02-27T14:16:47Z en_GB
dc.date.available 2011-01-25T10:33:14Z en_US
dc.date.available 2013-03-20T12:31:06Z
dc.identifier.issn 0002-9947 en_GB
dc.description Copyright © 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.journal Transactions of the American Mathematical Society en_GB


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