Dynamical behaviors and codings of invertible planar piecewise isometric systems

Yu, Rong-Zhong; Fu, Xinchu; Wang, Kan-Min; Chen, Zhanhe

doi:10.1016/j.na.2009.12.036

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“…In [18,20] the stability of periodic points of piecewise isometries defind on the Euclidean space has investigated and in [14] proved that piecewise isometries in arbitrary dymensional Euclidean space have zero topologica entropy. In [19,33] confirmed the existence of essntial coding for a forward singular point and present a necessary and sufficant condition for the existence of a admissible rational coding for a planar piecewise isometric map.…”

Section: Introductionmentioning

confidence: 70%

A System of Planar Piecewise Isometric Systems and Codings of These Systems

Sharifipour¹,

Mohammadinejad²

2017

Int. J. of Pure and Appl. Math.

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In this paper we investigate dynamics of a system of planar piecewise isometric systems. At first we introduce a coding map on a system of planar piecewise isometric systems then we extend the coding map onto the entire phase space and prove that there exist an essential coding for a singular point. At the end of this paper we investigate some important sets including singular sets, exceptional sets, rational sets, etc... generated by a system of planar piecewise isometric systems.

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