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Now showing items 1-7 of 7

  • Invariant sets for discontinuous parabolic area-preserving torus maps 

    Ashwin, Peter; Fu, Xin-Chu; Nishikawa, Takashi; Zyczkowski, Karol (Institute of Physics, 2000)
    We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter ...
  • On the geometry of orientation-preserving planar piecewise isometries 

    Ashwin, Peter; Fu, Xin-Chu (Springer, 2002)
    Planar piecewise isometries (PWIs) are iterated mappings of subsets of the plane that preserve length (and hence angle and area) on each of a number of disjoint regions. They arise naturally in several applications and are ...
  • Properties of the invariant disk packing in a model bandpass sigma-delta modulator 

    Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan (13 (3), pp. 631-641, 2003)
    In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space ...
  • Riddling and invariance for discontinuous maps preserving Lebesgue measure 

    Ashwin, Peter; Fu, Xin-Chu; Terry, John R. (Institute of Physics, 2002)
    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 ...
  • Symbolic analysis for some planar piecewise linear maps 

    Fu, Xin-Chu; Ashwin, Peter (American Institute of Mathematical Sciences, 2003)
    In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the ...
  • Symbolic representation of iterated maps 

    Fu, Xin-Chu; Lu, Weiping; Ashwin, Peter; Duan, Jinqiao (Schauder University Centre for Nonlinear Studies, 2001)
    This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map ...
  • Tangencies in invariant disc packings for certain planar piecewise isometries are rare 

    Ashwin, Peter; Fu, Xin-Chu (Taylor & Francis, 2001)
    For planar piecewise isometries (PWIs) (two-dimensional maps that restrict to isometries on some partition) there is a natural coding given by the itinerary of a trajectory between the pieces (atoms) of the partition on ...