Exact dimensionality of stationary measures for nonuniformly conformally contracting random diffeomorphisms
Preprint · arXiv:2609.10538
Dynamical Systems
Ergodic Theory
Dimension Theory
Subhasish Mukherjee. “Exact dimensionality of stationary measures for nonuniformly conformally contracting random diffeomorphisms.” Preprint, 2026.
Abstract
We prove exact dimensionality of ergodic stationary measures for random \(C^1\) diffeomorphisms in the single negative Lyapunov scale setting. Let \(\nu\) be a Borel probability measure on \(\operatorname{Diff}^1(M)\) satisfying a logarithmic \(C^1\) moment condition, and let \(\mu\) be a \(\nu\)-stationary ergodic probability measure. If \(\lambda_{\mathrm{top}} = \lambda_{\mathrm{bot}} = \lambda < 0\), then \(\mu\) is exact dimensional and \(\dim(\mu) = h_\mu^{\mathrm{F}}(\nu)/(-\lambda)\). No discreteness assumption is imposed on the driving measure.