## Tsukuba Journal of Mathematics

### Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set

Takashi Shimomura

#### Abstract

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

#### Article information

Source
Tsukuba J. Math., Volume 36, Number 2 (2013), 173-183.

Dates
First available in Project Euclid: 21 January 2013

https://projecteuclid.org/euclid.tkbjm/1358776997

Digital Object Identifier
doi:10.21099/tkbjm/1358776997

Mathematical Reviews number (MathSciNet)
MR3058237

Zentralblatt MATH identifier
1278.37019

#### Citation

Shimomura, Takashi. Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set. Tsukuba J. Math. 36 (2013), no. 2, 173--183. doi:10.21099/tkbjm/1358776997. https://projecteuclid.org/euclid.tkbjm/1358776997