Transitive sensitive subsystems for interval maps
Volume 169 / 2005
Studia Mathematica 169 (2005), 81-104
MSC: Primary 37E05.
DOI: 10.4064/sm169-1-6
Abstract
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.
