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Invariant circles for the piecewise linear standard map

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Abstract

We investigate invariant circles for a one-parameter family of piecewise linear twist homeomorphisms of the annulus. We show that invariant circles of all types and rotation numbers occur and we classify them into families. We compute parameter ranges in which there are no invariant circles.

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  1. School of Mathematical Sciences, Queen Mary College, University of London, Mile End Road, E1 4NS, London, United Kingdom

    Shaun Bullett

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  1. Shaun Bullett
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Communicated by J. Mather

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Bullett, S. Invariant circles for the piecewise linear standard map. Commun.Math. Phys. 107, 241–262 (1986). https://doi.org/10.1007/BF01209394

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  • DOI: https://doi.org/10.1007/BF01209394

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