Related papers: Geodesic flow for CAT(0)-groups

In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space…

We study those groups that act properly discontinuously, cocompactly, and isometrically on CAT(0) spaces with isolated flats and the Relative Fellow Traveller Property. The groups in question include word hyperbolic CAT(0) groups as well as…

We prove a logarithm law-type result for the spiraling of geodesics around certain types of compact subsets (e.g. quotients of periodic Morse flats) in quotients of rank one CAT(0) spaces.

In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of $M$ for which the pressure…

Using the works of Ma\~n\'e \cite{Ma} and Paternain \cite{Pat} we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a $\mathcal{C}^{\infty}$ Riemannian…

An explanation of stability of fireballs is proposed based on quantum effects in a thin surface layer of negatively charged plasma surrounding a positive kernel of a fireball. We construct a quantization of the geodesic flow on the sphere…

We describe a higher dimensional analogue of the Stallings folding sequence for group actions on CAT(0) cube complexes. We use it to give a characterization of quasiconvex subgroups of hyperbolic groups which act properly co-compactly on…

Ballmann's Rank Rigidity Conjecture predicts that a CAT(0) space of higher rank with a geometric group action is rigid -- isometric to a Riemannian symmetric space, a Euclidean building, or splits as a direct product. We confirm this…

Let $M$ be a closed, negatively curved Riemannian manifold of dimension $n \neq 4, 8$ with strictly $1/4$-pinched sectional curvature. We prove, that if the frame flow is ergodic and the sum of its unstable and stable bundles together with…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, let $O$ be an open subset of $X$, and let $F = \{g_t: t\ge 0\}$ be a one-parameter subsemigroup of $G$. Consider the set of points in $X$ whose $F$-orbit misses…

We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundle. We show a correspondence between normal trajectories and…

It is shown that the renormalisation group flow in coupling constant space can be interpreted in terms of a dynamical equation for the couplings analogous to viscous fluid flow under the action of a potential. For free scalar field theory…

We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere with a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we…

Motivated by Gromov's geodesic flow problem on hyperbolic groups $G$, we develop in this paper an analog using random walks. This leads to a notion of a harmonic analog $\Theta$ of the Bowen-Margulis-Sullivan measure on $\partial^2 G$. We…

We prove that the geodesic flow on a locally CAT(-1) metric space which is compact, or more generally convex cocompact with non-elementary fundamental group, can be coded by a suspension flow over an irreducible shift of finite type with…

We prove that the geodesic flow on a compact locally CAT(-1) space has the weak specification property, and give various applications. We show that every H\"older potential on the space of geodesics has a unique equilibrium state. We…

We study the geodesic flow of a compact surface without conjugate points and genus greater than one and continuous Green bundles. Identifying each strip of bi-asymptotic geodesics induces an equivalence relation on the unit tangent bundle.…

As an absolute invariant of smooth conjugacy, the multiplier group described the types of space-time symmetries that the flow has, and for a quasiperiodic flow on the $n$-torus, is the determining factor of the structure of its generalized…

The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corresponds to the superdiagonal. We prove that the associated…

Let $Q$ be a closed manifold admitting a locally-free action of a compact Lie group $G$. In this paper we study the properties of geodesic flows on $Q$ given by Riemannian metrics which are invariant by such an action. In particular, we…