arXiv subjects

Daniel Mitsutani

Publications and source records attributed to Daniel Mitsutani.

4 recordsLinked to original sources

arXiv2025

Monotonicity of the Liouville entropy along the Ricci flow on surfaces

We show that the Liouville entropy of the geodesic flow of a closed surface of non-constant negative curvature is eventually strictly increasing along the normalized Ricci flow (NRF). More precisely, we obtain a new expression for the derivative of the Liouville entropy along an arbitrary conformal deformation in dimension 2, and we prove it is positive in the direction of the NRF for 1/6-pinched metrics. This partially answers a question of Manning from 2004. In addition, we show that the mean root curvature, a purely geometric quantity which is a lower bound for the Liouville entropy, is strictly increasing along the NRF starting from any metric of non-constant negative curvature.

math.DS↗

arXiv2024

Symmetries of geodesic flows on covers and rigidity

We define and study the foliated centralizer: the group of $C^\infty$ centralizer elements of the lift of an Anosov system on a non-compact manifold which additionally preserve the stable and unstable foliations. When the Anosov system is the geodesic flow of a closed Riemannian manifold with pinched negative sectional curvatures, we prove some rigidity properties for the foliated centralizer of the lift of the flow to the universal cover: it is a finite-dimensional Lie group, which is moreover discrete (modulo the action of the flow itself) unless the metric is homothetic to some real hyperbolic metric. This result is inspired by the study of isometries of universal covers that appeared originally in the work of Eberlein, and later in Farb and Weinberger, as well as centralizer rigidity results in dynamics.

math.DS↗

arXiv2023

Coexistence of measures with simple Lyapunov spectrum for fiber-bunched cocycles

We prove that if a Hölder continuous fiber-bunched cocycle $\hat{A}$ over an invertible hyperbolic transitive shift $\hatΣ$ satisfies an appropriate strong irreducibility condition on Grassmannians, then $\hatΣ$ admits an ergodic measure $\hatμ$ with full support and product structure with simple Lyapunov spectrum if and only if any other ergodic measure with full support and product structure also has simple Lyapunov spectrum.

math.DS↗

arXiv2021

Simplicity of the Lyapunov Spectrum for classes of Anosov flows

We prove that in a $C^1$-open and $C^k$-dense set of some classes of $C^k$ Anosov flows all Lyapunov exponents have multiplicity 1 with respect to appropriate measures. The classes are geodesic flows with equilibrium states of Hölder-continuous potentials, volume-preserving flows, and all fiber-bunched Anosov flows with equilibrium states of Hölder-continuous potentials. In the proof, we use and prove perturbative results for jets of flows to modify eigenvalues of certain Poincaré maps and, using a Markov partition, apply the simplicity criterion of Avila and Viana.

math.DS↗