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We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation…

Geometric Topology · Mathematics 2015-06-26 Danny Calegari

We show that every irreducible, simply connected curve on a toric affine surface X over the field of complex numbers is an orbit closure of a multiplicative group action on X. It follows that up to the action of the automorphism group…

Algebraic Geometry · Mathematics 2013-07-18 I. Arzhantsev , M. Zaidenberg

We study projectivity in the category of $G$-flows and affine $G$-flows for Polish groups $G$. We also introduce the notion of \emph{proximally irreducible} extensions between affine $G$-flows. Using this we provide a characterization of…

Dynamical Systems · Mathematics 2025-11-21 Jashan Bal

We consider the topological dynamics of the automorphism group of a particular sparse graph M_1 resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on M_1 have all orbits meagre,…

Logic · Mathematics 2026-05-06 Rob Sullivan

In this paper we discuss a coding and the associated symbolic dynamics for the geodesic flow on Hecke triangle surfaces. We construct an explicit cross section for which the first return map factors through a simple (explicit) map given in…

Dynamical Systems · Mathematics 2008-01-28 Dieter Mayer , Fredrik Strömberg

We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with H\"older Jacobians. In the same setting, we give a precise…

Dynamical Systems · Mathematics 2023-04-27 Pablo D. Carrasco , Federico Rodriguez-Hertz

Let (M,g) be a compact Riemannian manifold of hyperbolic type, i.e M is a manifold admitting another metric of strictly negative curvature. In this paper we study the geodesic flow restricted to the set of geodesics which are minimal on the…

Differential Geometry · Mathematics 2013-08-12 Gerhard Knieper , Carlos Ogouyandjou , Jan Philipp Schröder

We study the holonomy cocycle H of a holomorphic foliation \Fc by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: 1) its singularities E are all hyperbolic; 2) there is no…

Dynamical Systems · Mathematics 2017-12-27 Viet-Anh Nguyen

We define recurrence for a compactly generated para-topological group $G$ acting continuously on a locally compact Hausdorff space $X$ with $\dim X=0$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i)…

Dynamical Systems · Mathematics 2022-07-26 Xiongping Dai

We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost…

Dynamical Systems · Mathematics 2024-07-22 Alejo García-Sassi , Pierre-Antoine Guihéneuf , Pablo Lessa

Given two hyperbolic surfaces and a homotopy class of maps between them, Thurston proved that there always exists a representative minimizing the Lipschitz constant. While not unique, these minimizers are rigid along a geodesic lamination.…

Geometric Topology · Mathematics 2025-10-24 Aaron Calderon , Jing Tao

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for…

Mathematical Physics · Physics 2008-12-23 Alexey V. Bolsinov , Bozidar Jovanovic

In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting element. We show that the existence of a contracting isometry is…

Dynamical Systems · Mathematics 2025-10-28 Rémi Coulon

Let X be an infinite Riemann surface with an upper-bounded geodesic pants decomposition. The vertices of the corresponding dual graph G are pairs of pants and edges are cuffs with conductances equal to their lengths. We prove that the…

Dynamical Systems · Mathematics 2026-05-06 Charles Bordenave , Xinlong Dong , Dragomir Šarić

We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary…

Differential Geometry · Mathematics 2009-10-31 Francois Labourie

We introduce a description of a minimal surface in a space with boundary, as the world-hypersurface that the entangling surface traces. It does so by evolving from the boundary to the interior of the bulk under an appropriate geometric…

High Energy Physics - Theory · Physics 2020-04-22 Dimitrios Katsinis , Ioannis Mitsoulas , Georgios Pastras

Our interest in this work is in group extensions of minimal flows with compact abelian groups in the fibres. We study their structure from categorical and algebraic points of view, and describe relations of their dynamics to the…

Dynamical Systems · Mathematics 2021-01-13 Matúš Dirbák

The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of…

Differential Geometry · Mathematics 2019-09-17 James Kohout , Melanie Rupflin , Peter M. Topping

By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique…

Differential Geometry · Mathematics 2024-03-25 Benjamin Delarue , Daniel Monclair , Andrew Sanders

These notes are based on lectures given by the author at the Summer School on Teichm\"uller dynamics, mapping class groups and applications in Grenoble, France, in June 2018 and at the Oberwolfach Seminar on Anisotropic Spaces and their…

Dynamical Systems · Mathematics 2020-07-08 Giovanni Forni