Differentiable circle maps with a flat interval |
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| Authors: | J Graczyk L B Jonker G ?wi?tek F M Tangerman J J P Veerman |
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| Institution: | (1) Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland;(2) Department of Mathematics and Statistics, Queen's University, K7L 3N6 Kingston, ON, Canada;(3) Mathematics Department, Princeton University, 08544 Princeton, NJ, USA;(4) Institute of Mathematical Sciences, SUNY at Stony Brook, 11794 Stony Brook, NY, USA;(5) Depto de matematica, U.F.P.E., Cidade Universitaria, Rua Prof. Luis Freire, 50740-540 Recife, PE, Brazil |
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| Abstract: | We study weakly order preserving circle maps with a flat interval, which are differentiable even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set. Also, a sharp transition is found from degenerate geometry to bounded geometry, depending on the degree of the singularities at the boundary of the flat interval.Partially supported by KBN grant  Iteracje i Fraktale #210909101. |
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