English

Rotation sets and almost periodic sequences

Dynamical Systems 2014-08-14 v1

Abstract

We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segments as well as non-convex and even plane-separating continua. This shows that restrictions holding for rotation sets on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the problem to a symbolic level, where the desired rotational behaviour is implemented by means of suitable irregular Toeplitz sequences.

Keywords

Cite

@article{arxiv.1408.2931,
  title  = {Rotation sets and almost periodic sequences},
  author = {Tobias Jäger and Alejandro Passeggi and Sonja Štimac},
  journal= {arXiv preprint arXiv:1408.2931},
  year   = {2014}
}
R2 v1 2026-06-22T05:27:27.801Z