Critical curves of a piecewise linear map

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  • John A. G. Roberts
    School of Mathematics and Statistics, University of New South Wales 1 , Sydney, New South Wales 2052, Australia
  • Asaki Saito
    Future University Hakodate 2 , 116-2 Kamedanakano-cho, Hakodate, Hokkaido 041-8655, Japan
  • Franco Vivaldi
    School of Mathematical Sciences, Queen Mary, University of London 3 , London E1 4NS, United Kingdom

Description

<jats:p>We study the parameter space of a family of planar maps, which are linear on each of the right and left half-planes. We consider the set of parameters for which every orbit recurs to the boundary between half-planes. These parameters consist of algebraic curves, determined by the symbolic dynamics of the itinerary that connects boundary points. We study the algebraic and geometrical properties of these curves, in relation to such a symbolic dynamics.</jats:p>

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