The entropy conjecture for dominated splitting with multi 1D centers via upper semi-continuity of the metric entropy. (28th June 2017) - Zang, Yuntao; Yang, Dawei; Cao, Yongluo
Abstract: Let f be a C 1 diffeomorphism on a compact manifold M, Λ be a compact invariant subset with a dominated splitting T Λ M = E c u ⊕ > E 1 ⊕ > E 2 ⋯ ⊕ > E l ⊕ > E c s such that dim E i = 1 ( 1 ⩽ i ⩽ l ) and for any invariant probability measure ν, the Lyapunov exponents of ν are non-negative along E cu and non-positive along E cs . Then the entropy conjecture is true in this setting as a consequence of the upper semi-continuity of the metric entropy.