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

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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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