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Transitive sensitive subsystems for interval maps
2005
Studia Mathematica
We prove that for continuous interval maps the existence of a non-empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke, and we exhibit examples showing that these three notions are distinct. [81] Recently, Blanchard, Glasner, Kolyada and Maass [4] proved that, if T : X → X is a continuous map on the compact metric space X such that the topological entropy of T is positive, then
doi:10.4064/sm169-1-6
fatcat:4ntuvkybnjgpzaunsckodzu4na