The Globally Attracting and Repelling for a Class of Planar Piecewise Isometries

The authors investigate the globally attracting and repelling for planar piecewise isometric system in this paper. Firstly, we get two fundamental propositions about globally attracting and repelling for general piecewise isometry defined on the entire planar. Secondly, we discuss the attracting and repelling of a class of planar piecewise isometry with section partition by the similar way as the paper (Michael Boshernitzan and Arek Goetz "A dichotomy for a two-parameter piecewise rotation" Ergodic Theory and Dynamical Systems, 2003,23,(3) pp. 759-777.). In fact, the main result in this paper is the generalization of the one in above paper.