## Tsukuba Journal of Mathematics

### Chain mixing endomorphisms are approximated by subshifts 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 a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, homeomorphisms that are topologically conjugate to g approximate f in the topology of uniform convergence if a trivial necessary condition on the periodic points holds. In particular, if f is a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point, then homeomorphisms on the Cantor set that are topologically conjugate to a subshift approximate f in the topology of uniform convergence. In addition, homeomorphisms on the Cantor set that are topologically conjugate to a subshift without periodic points approximate any chain mixing continuous onto mappings from the Cantor set onto itself. In particular, let f be a homeomorphism on the Cantor set that is topologically conjugate to a full shift. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, a sequence of homeomorphisms that is topologically conjugate to g approximates f.

#### Article information

Source
Tsukuba J. Math., Volume 35, Number 1 (2011), 67-77.

Dates
First available in Project Euclid: 19 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1311081449

Digital Object Identifier
doi:10.21099/tkbjm/1311081449

Mathematical Reviews number (MathSciNet)
MR2848816

Zentralblatt MATH identifier
1237.37015

#### Citation

Shimomura, Takashi. Chain mixing endomorphisms are approximated by subshifts on the Cantor set. Tsukuba J. Math. 35 (2011), no. 1, 67--77. doi:10.21099/tkbjm/1311081449. https://projecteuclid.org/euclid.tkbjm/1311081449