Tsukuba Journal of Mathematics

Chain mixing endomorphisms are approximated by subshifts on the Cantor set

Takashi Shimomura

Full-text: Open access

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

Subjects
Primary: 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

Keywords
Cantor set shift subshift subshift of finite type chain mixing approximation

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


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