Transitive, sensitive subsystems for interval maps

Studia Math. , 169, No. 1, 81-104, 2005.


We state 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.

Paper: [arXiv:1901.01067] [pdf (published paper)]