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When is a composition of homeomorphisms topologically transitive provided one of the two is?
Suppose that $S$ is a (connected) regular surface, possibly with boundary, for instance an annulus. Suppose that both $f$ and $g$ are homeomorphisms whose restriction to $\partial S$ is the identity. ...
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State of the art on: "If a dynamical system is Li-Yorke chaotic, does there exist a Cantor scrambled set?"
The following problem is presented in the paper Recent development of chaos theory in topological dynamics - by Jian Li and Xiangdong Ye :
"If a dynamical system [$(X,f)$, $X$ metric space, $f$ ...
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