Year: 2026
Type: preprint
Abstract: We establish a general criterion on the upper semi-continuity of partial entropy in all directions for $C^{1+α}$ 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 $C^{1+α}$ diffeomorphism, which extends the $C^{\infty}$ 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.
Source: arXiv (Cornell University)
Authors: Liao, Gang, Tao, Huirong, Tong, Yao, Yang, Jiagang
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161118239
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