Abstract
Trapezoidal maps which are everywhere expanding out of their plateau form a three parameter familyT, up to affine changes of coordinates. We show that splittingT according to the various possible dynamical “behaviors” (we make this word precise in the process), yields a codimension one foliation. Some consequences of our result in terms of the monotonicity along simple one parameter families inT are then drawn. All together, aperiodic behavior is rare both from the topological and the measure theoretical point of view inT.
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Communicated by J.-P. Eckmann
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Brucks, K.M., Misiurewicz, M. & Tresser, C. Monotonicity properties of the family of trapezoidal maps. Commun.Math. Phys. 137, 1–12 (1991). https://doi.org/10.1007/BF02099114
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DOI: https://doi.org/10.1007/BF02099114