Monotone maps of 𝐺-like continua with positive topological entropy yield indecomposability

Kato, Hisao

doi:10.1090/proc/14602

Monotone maps of $G$-like continua with positive topological entropy yield indecomposability
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Proc. Amer. Math. Soc. 147 (2019), 4363-4370 Request permission

Abstract:

In the previous paper Adv. Math. 304 (2017), pp. 793–808, we proved that if for any graph $G$, a homeomorphism on a $G$-like continuum $X$ has positive topological entropy, then the continuum $X$ contains an indecomposable subcontinuum. Also, if for a tree $G$, a monotone map on a $G$-like continuum $X$ has positive topological entropy, then the continuum $X$ contains an indecomposable subcontinuum. In this note, we extend these results. In fact, we prove that if for any graph $G$, a monotone map on a $G$-like continuum $X$ has positive topological entropy, then the continuum $X$ contains an indecomposable subcontinuum. Also we study topological entropy of monotone maps on Suslinean continua.

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