October  1998, 4(4): 593-608. doi: 10.3934/dcds.1998.4.593

Dynamics of a piecewise rotation

1. 

Department of Mathematics, Boston University, 111 Cummington St., Boston, Ma. 02215, United States

Received  September 1997 Revised  February 1998 Published  July 1998

We investigate the dynamics of systems generalizing interval exchanges to planar mappings. Unlike interval exchanges and translations, our mappings, despite the lack of hyperbolicity, exhibit many features of attractors. The main result states that for a certain class of noninvertible piecewise isometries, orbits visiting both atoms infinitely often must accumulates on the boundaries of the attractor consisting of two maximal invariant discs $D_0 \cup D_1$ fixed by $T$. The key new idea is a dynamical and geometric observation about the monotonic behavior of orbits of a certain first-return map. Our model emerges as the local map for other piecewise isometries and can be the basis for the construction of more complicated molecular attractors.
Citation: Arek Goetz. Dynamics of a piecewise rotation. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 593-608. doi: 10.3934/dcds.1998.4.593
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