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Curlicues generated by circle homeomorphisms

机译:圆同构生成的曲面

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摘要

We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction expansion, existence of a continuous solution of the corresponding cohomological equation and displacement sequence along the orbit.
机译:我们研究了复平面中的曲线,这些曲线是由实数序列生成的,实数是保持圆同构的方向轨道上点的升力。这些曲线的几何性质,如有界性、表面性、局部离散曲率半径,与产生它们的圆同构的动力学性质有关:旋转数及其持续的分数展开,相应同调方程的连续解的存在和沿轨道的位移序列。

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