Year 2022

• 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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Year 2016

• Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds

  Publication

  • G. Graff
  • J. Jezierski

  - GEOMETRIAE DEDICATA - Year 2016

  Let M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...

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