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Scalings in circle maps III

Jacek Graczyk·Grzegorz Swiatek·Folkert Tangerman·J. J. P. Veerman
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Abstract

Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found from degenerate geometry similar to what was found earlier for non-differentiable maps with a flat spot to bounded geometry as in critical maps without a flat spot.

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Jacek Graczyk, Grzegorz Swiatek, Folkert Tangerman, J. J. P. Veerman. 1992-02-03. Scalings in circle maps III. https://arxiv.org/abs/math/9202209

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