Tubular Dimension: Leaf-Wise Asymptotic Local Product Structure, and Entropy and Volume Growth
Abstract
Abstract We study the conditional measures of every invariant probability measure for every $$C^{1+\gamma }$$ C 1 + γ diffeomorphism of a closed Riemannian manifold, and we show that they always admit an asymptotic local product structure. This is a direct application of the notion of tubular dimension which we introduce and study in the manuscript. As an additional application we prove a bound on any two consecutive conditional entropies in terms of volume growth.
Fields of Study & Subjects
Theoretical and Computational Physics
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 8
- Publication date
- 20 July 2026
- Language
- EN