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A piecewise linear model for the zones of instability of an area- preserving map. (English) Zbl 0588.58009

The transformation \(F(x,y)=(1-y+| x|,x)\) has a dense set of periodic points in the plane (since it leaves invariant denominators), it has an elliptic fixed point with invariant polygons surrounding it, in between these polygons it has invariant (nonuniformly) hyperbolic sets with stable and unstable manifolds being (locally) straight lines.... For this map in contrast to smooth ones all these facts can be explicitly calculated by elementary means, giving the author reason to promote the investigation of piecewise linear maps as models for smooth ones.
Reviewer: H.Crauel

MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
26A18 Iteration of real functions in one variable
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