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.
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Communicated by J.-P. Eckmann
Partially supported by KBN grant ‘Iteracje i Fraktale’ #210909101.
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Graczyk, J., Jonker, L.B., Świątek, G. et al. Differentiable circle maps with a flat interval. Commun.Math. Phys. 173, 599–622 (1995). https://doi.org/10.1007/BF02101658
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DOI: https://doi.org/10.1007/BF02101658