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.
Citation
Takashi Shimomura. "Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set." Tsukuba J. Math. 36 (2) 173 - 183, December 2012. https://doi.org/10.21099/tkbjm/1358776997
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