6 papers
Rigidity of the dynamics of on representations into a compact group
Serge Cantat, Christophe Dupont, Florestan Martin-Baillon
Let be a compact Lie group. Let be the free group of rank . We describe the orbits of on whe…
Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity
Pierre Houedry, Nicolas Courty, Florestan Martin-Baillon +2
Trees and the associated shortest-path tree metrics provide a powerful framework for representing hierarchical and combinatorial structures in data. Given an arbitrary metric space…
Dynamics on Markov surfaces: classification of stationary measures
Serge Cantat, Christophe Dupont, Florestan Martin-Baillon
Consider the four punctured sphere . Each choice of four traces, one for each puncture, determines a relative character variety for the representations of the fun…
Gap between Lyapunov exponents for Hitchin representations
Matteo Costantini, Florestan Martin-Baillon
We study Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We consider them as invariants on the space of Hitchin re…
Dominating CAT(-1) surface group representations by Fuchsian ones
Florestan Martin-Baillon
We show that for every representation of the fundamental group of a genus surface to the isometry group of a complete $ \text{CA…
Lyapunov exponents and stability properties of higher rank representations
Florestan Martin-Baillon
Generalizing results of Deroin-Dujardin, we introduce the notion of proximal stability for a holomorphic family of representations , wher…