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Full-Text Articles in Physical Sciences and Mathematics
Differentiable Circle Maps With A Flat Interval, J. Graczyk, L. B. Jonker, G. Swiatek, F. M. Tangerman, J. J. P. Veerman
Differentiable Circle Maps With A Flat Interval, J. Graczyk, L. B. Jonker, G. Swiatek, F. M. Tangerman, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
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.
Intersecting Self-Similar Cantor Sets, J. J. P. Veerman
Intersecting Self-Similar Cantor Sets, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We define a self-similar set as the (unique) invariant set of an iterated function system of certain contracting affine functions. A topology on them is obtained (essentially) by inducing the C 1- topology of the function space. We prove that the measure function is upper semi-continuous and give examples of discontinuities. We also show that the dimension is not upper semicontinuous. We exhibit a class of examples of self-similar sets of positive measure containing an open set. If C 1 and C 2 are two self-similar sets C 1 and C 2 such that the sum of their dimensions …