Robust Transitivity of Partially Hyperbolic Diffeomorphisms with Interval Central Leaves

Abstract

For a boundary-preserving partially hyperbolic diffeomorphism with interval central leaves, we completely characterize the $C^k$-robust transitivity $(k\ge 2)$ by boundary interconnection. As an application, if the boundary SRB measures admit negative central Lyapunov exponents, then boundary interconnection also completely characterizes the phenomenon of robustly intermingled basins for boundary SRB measures.

v1: 25 pages, 8 figures; v2: 26 pages, 8 figures (mainly fix Lemma 2.5 and several typos, and update some explanations). Comments are welcome!