Year: 2026
Type: preprint
Abstract: We show that every Anosov diffeomorphism is topologically expansive in the sense of [9]. We also prove that Lipschitz shadowing forces the stable and unstable bundles to be uniformly transverse, with a quantitative bound in terms of the shadowing constant. Finally, we give two examples on complete Riemannian manifolds: one is expansive but does not have the shadowing property, while the other has finite volume, bounded sectional curvature, Lipschitz shadowing, and orthogonal invariant bundles, but is not expansive with respect to its Riemannian distance.
Source: arXiv (Cornell University)
Authors: Li, Z., Morales, C. A., Romaña, S., Yang, Y.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4659911933
OpenAlex ID: W7213248733