6 citations · 25 across the 18 of their papers we have counts for
18 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 theorem…
The distribution of critical graphs of Jenkins-Strebel differentials
Francisco Arana-Herrera, Aaron Calderon
By work of Jenkins and Strebel, given a Riemann surface X and a simple closed multi-curve on it, there exists a unique quadratic differential q on X whose horizontal foliation…
The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics
Francisco Arana-Herrera, Aaron Calderon
Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of th…
Effective count of square-tiled surfaces with prescribed real and imaginary foliations in connected components of strata
Francisco Arana-Herrera
We prove an effective estimate with a power saving error term for the number of square-tiled surfaces in a connected component of a stratum of quadratic differentials whose vertica…
Counting problems from the viewpoint of ergodic theory: from primitive integer points to simple closed curves
Francisco Arana-Herrera
In her thesis, Mirzakhani showed that the number of simple closed geodesics of length on a closed, connected, oriented hyperbolic surface of genus is asymptotic to…
The asymmetry of Thurston's earthquake flow
Francisco Arana-Herrera, Alex Wright
We show that Thurston's earthquake flow is strongly asymmetric in the sense that its normalizer is as small as possible inside the group of orbifold automorphisms of the bundle of…
Bounds on the Hausdorff dimension of Teichmüller horocycle flow orbit closures
Francisco Arana-Herrera
We show that the Hausdorff dimension of any proper Teichmüller horocycle flow orbit closure on any -invariant subvariety of Abelian or quadratic differ…
Effective mapping class group dynamics III: Counting filling closed curves on surfaces
Francisco Arana-Herrera
We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length on an arbitrary closed, o…
Effective mapping class group dynamics II: Geometric intersection numbers
Francisco Arana-Herrera
We show that the action of the mapping class group on the space of closed curves of a closed surface effectively tracks the corresponding action on Teichmüller space in the followi…
Effective mapping class group dynamics I: Counting lattice points in Teichmüller space
Francisco Arana-Herrera
We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichmüller space that lie within a Teichmüller metric ba…
Counting hyperbolic multi-geodesics with respect to the lengths of individual components
Francisco Arana-Herrera
Given a connected, oriented, complete, finite area hyperbolic surface of genus with punctures, Mirzakhani showed that the number of multi-geodesics on of total hype…
Equidistribution of horospheres on moduli spaces of hyperbolic surfaces
Francisco Arana-Herrera
Given a simple closed curve on a connected, oriented, closed surface of negative Euler characteristic, Mirzakhani showed that the set of points in the moduli space of hyper…
Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfaces
Francisco Arana-Herrera, Jayadev S. Athreya
Given integers satisfying , let be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus with…
Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics
Francisco Arana-Herrera
We show that the number of square-tiled surfaces of genus , with marked points, with one or both of its horizontal and vertical foliations belonging to fixed mapping class g…