The entropy conjecture for dominated splitting with multi 1D centers via upper semi-continuity of the metric entropy. (28th June 2017)

• Record Type: Journal Article
• Authors: Zang, Yuntao; Yang, Dawei; Cao, Yongluo
• Is Part Of: Nonlinearity. Volume 30:Number 8(2017:Aug.)
• Page Start: 3076
• Page End: 3087
• Publication Date: 2017-06-28
• Subjects: dominates splitting -- metric entropy -- upper semi-continuous; 37D25 -- 37D30 -- 37D35 -- 37B40; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa773c
• Languages: English
• ISSNs: 0951-7715

Abstract

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.