Continuity properties of partial entropy
摘要
We establish a general criterion on the upper semi-continuity of partial entropy in all directions for diffeomorphisms: it holds when the respective sums of Lyapunov exponents are continuous. This addresses, in arbitrary dimensions, the converse aspect of the entropic continuity of the Lyapunov exponents established by Buzzi, Crovisier, and Sarig. Consequently, the entropy (and all the partial entropies) is always upper semi-continuous at generic ergodic measures of every diffeomorphism, which extends the result of Newhouse. Numerous applications and examples are provided, including topics related to measures with dominated splittings, SRB measures, average expanding diffeomorphisms, singular flows, standard maps, and symbolic codings for diffeomorphisms.
引用
@article{arxiv.2605.13273,
title = {Continuity properties of partial entropy},
author = {Gang Liao and Huirong Tao and Yao Tong and Jiagang Yang},
journal= {arXiv preprint arXiv:2605.13273},
year = {2026}
}