Search results for: curlicues

• Curlicues generated by circle homeomorphisms

  Publication

  • J. Signerska-Rynkowska

  - GEOMETRIAE DEDICATA - Year 2022

  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...

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• On Computing Curlicues Generated by Circle Homeomorphisms

  Publication

  • J. Signerska-Rynkowska

  - Year 2022

  The dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the...

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• Computing dynamical curlicues

  Open Research Data

  open access

  • J. Signerska-Rynkowska
  • G. Graff

  A curlicue is a piece-wise linear curve in the complex plane which can be generated by an arbitrary sequence of real numbers u_n. It can be interpreted as a trajectory of a particle in the plane which starts in the origin at time t=0 and moves with a constant velocity, changing its direction at instances t=0,1,2,3,..., where the new direction is given...