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On codings and dynamics of planar piecewise rotations. (English) Zbl 1246.37064
Summary: We investigate codings and dynamics of piecewise rotations belonging to a sub-class of piecewise isometries. We show that the irrational set is empty for some piecewise rational rotations under some assumptions, while a piecewise irrational rotation has at least one irrational coding by extending the definition of the coding map onto the entire phase space. We further prove that the cell corresponding to irrational coding is a single point set for a piecewise irrational rotation.
MSC:
 37E30 Homeomorphisms and diffeomorphisms of planes and surfaces 37E45 Rotation numbers and vectors 37B10 Symbolic dynamics