Year: 2026
Type: preprint
Abstract: In this paper, we study \(C^{1+α}\) diffeomorphisms of a compact Riemannian manifold \(\mathbf{M}\) with an attracting set \(Λ\) admitting a partially hyperbolic splitting \[ T_Λ\mathbf{M} = E^u\oplus C_1\oplus\cdots\oplus C_k\oplus E^s. \] We assume that, for every ergodic Gibbs \(u\)-state supported on \(Λ\), the Lyapunov exponents along each \(C_i\) are either all positive or all negative. We prove that \(Λ\) supports finitely many ergodic hyperbolic SRB measures whose basins cover Lebesgue almost every point of its topological basin. Our approach relies on an empirical basin-covering theorem for attracting sets with dominated splittings. Its proof hinges on a new notion of sliding suffix times, which allows us to synchronize expansion and contraction along a common empirical subsequence.
Source: arXiv (Cornell University)
Authors: Cao, Yongluo, Mi, Zeya
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G198454105, G3250800360
OpenAlex ID: W7223024519