English

Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set

Dynamical Systems 2015-06-26 v1

Abstract

Let ff be a chain mixing continuous onto mapping from the Cantor set onto itself.Let gg be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate ff in the topology of uniform convergence if a trivial necessary condition on periodic points is satisfied.In particular, let ff be a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point and g, an aperiodic homeomorphism on the Cantor set. Then, homeomorphisms that are topologically conjugate to gg approximate ff.

Keywords

Cite

@article{arxiv.1506.07663,
  title  = {Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set},
  author = {Takashi Shimomura},
  journal= {arXiv preprint arXiv:1506.07663},
  year   = {2015}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1506.06514

R2 v1 2026-06-22T10:00:00.166Z