5 papers
Chaos in large genus surfaces
Francisco Arana-Herrera
Geodesic flows on closed hyperbolic surfaces are a quintessential example of chaotic dynamics, i.e., systems whose long term behavior is very sensitive to initial conditions. The s…
Heisenberg Translation Flows
Francisco Arana-Herrera, Jayadev Athreya, Giovanni Forni
We study ergodic theoretical properties of flows on circle bundles over translation surfaces that arise via prequantization, generalizing the theory of Heisenberg nilflows to base…
The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces
Francisco Arana-Herrera, Alex Wright
We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At…
Weak mixing in rational billiards
Francisco Arana-Herrera, Jon Chaika, Giovanni Forni
We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin,…
From limit theorems to mixing limit theorems
Francisco Arana-Herrera, Giovanni Forni
Motivated by work of Dolgopyat and Nándori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theore…