A report on an ergodic dichotomy Page 1 Ergod. Th. & Dynam. Sys., (2024), 44, 236–289 ©
The Author(s), 2023. Published by Cambridge University Press. This is an Open Access …

The François Massieu 1869 idea to derive some mechanical and thermal properties of
physical systems from “Characteristic Functions”, was developed by Gibbs and Duhem in …

Given a dynamical system with a uniformly hyperbolic (chaotic) attractor, the physically
relevant Sinaĭ–Ruelle–Bowen (SRB) measure can be obtained as the limit of the dynamical …

We prove that the geodesic flow on a geometrically finite locally symmetric space of negative
curvature is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure. The …

We develop a unified approach for establishing rates of decay for the Fourier transform of a
wide class of dynamically defined measures. Among the key features of the method is the …

We refine the recent local rigidity result for the marked length spectrum obtained by the first
and third author in [GL19] and give an alternative proof using the geodesic stretch between …

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have
unique equilibrium states for natural classes of potentials. In particular, we characterize the …

Let D− and D+ be properly immersed closed locally convex subsets of a Riemannian
manifold with pinched negative sectional curvature. Using mixing properties of the geodesic …

2 Negatively Curved Geometry 2.1 Background on CAT (− 1) spaces................... 23 2.2
Generalised geodesic lines....................... 29 2.3 The unit tangent bundle........................ 31 2.4 …

Let Γ be a Zariski-dense Kleinian Schottky subgroup of PSL 2 (C). Let Λ Γ⊂ C be its limit set,
endowed with a Patterson–Sullivan measure μ supported on Λ Γ. We show that the Fourier …