The entropy conjecture for dominated splitting with multi 1D centers via upper semi-continuity of the metric entropy

作者：Zang, Yuntao^*; Yang, Dawei; Cao, Yongluo

来源：Nonlinearity, 2017, 30(8): 3076-3087.

DOI：10.1088/1361-6544/aa773c

• dominates splitting
• metric entropy
• upper semi-continuous

Let f be a C-1 diffeomorphism on a compact manifold M, Lambda be a compact invariant subset with a dominated splitting T Lambda M = E-cu circle plus > E-1 circle plus > E-2 center dot center dot center dot circle plus > E-1 circle plus > E-cs such that dim Ei = 1(1 <= i <= l) and for any invariant probability measure., the Lyapunov exponents of. are non-negative along Ecu and nonpositive along Ecs. Then the entropy conjecture is true in this setting as a consequence of the upper semi-continuity of the metric entropy.

• 出版日期2017-8
• 单位苏州大学