Tsukuba Journal of Mathematics

Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set

Takashi Shimomura

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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

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1358776997

Digital Object Identifier
doi:10.21099/tkbjm/1358776997

Mathematical Reviews number (MathSciNet)
MR3058237

Zentralblatt MATH identifier
1278.37019

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

Keywords
Cantor set homeomorphism dynamical system chain mixing approximate conjugacy

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


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