Related papers: Dynamics of hyperbolic iwips

Let $\Gamma$ be a (convex-)cocompact group of isometries of the hyperbolic space $\mathbb{H}^d$, let $M := \mathbb{H}^d/\Gamma$ be the associated hyperbolic manifold, and consider a real valued potential $F$ on its unit tangent bundle $T^1…

The Einstein-Hilbert worldspace action is used to investigate the dynamics of extended object. In the Robertson-Walker worldspace, this is seen to introduce a pressureless density which could contribute to dark matter. Such pressureless…

In this paper we describe a function $F_n:{\bf R}_+ \to {\bf R}_{+}$ such that for any hyperbolic n-manifold $M$ with totally geodesic boundary $\partial M \neq \emptyset$, the volume of $M$ is equal to the sum of the values of $F_n$ on the…

We prove a radial source estimate in H\"older-Zygmund spaces for uniformly hyperbolic dynamics (also known as Anosov flows), in the spirit of Dyatlov-Zworski. The main consequence is a new linear stability estimate for the marked length…

Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroups $H$ of $G$. This is the main ingredient for proving that $P$…

In this note we construct a "restriction" map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to parabolic induction and deduce that…

Moduli spaces of hyperbolic surfaces with geodesic boundary components of fixed lengths may be endowed with a symplectic structure via the Weil-Petersson form. We show that, as the boundary lengths are sent to infinity, the Weil-Petersson…

We show that for any subgroup $H$ of Out($F_N$), either $H$ contains an atoroidal element or a finite index subgroup $H'$ of $H$ fixes a nontrivial conjugacy class in $F_N$. This result is an analog of Ivanov's subgroup theorem for mapping…

We show that large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic…

We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification…

We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material…

We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of…

We show that the motion on the n-dimensional ellipsoid is complete integrable by exhibiting n integrals in involution. The system is separable at classical and quantum level, the separation of classical variables being realized by the…

A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…

In this paper the author considers the motion of a relativistic perfect fluid with self-interaction mediated by Nordstrom's scalar theory of gravity. The evolution of the fluid is determined by a quasilinear hyperbolic system of PDEs, and a…

We show the equivalence of several characterizations of relative hyperbolicity for metric spaces, and obtain extra information about geodesics in a relatively hyperbolic space. We apply this to characterize hyperbolically embedded subgroups…

We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity,…

Let f be a non-invertible holomorphic endomorphism of a projective space and f^n its iterate of order n. We prove that the pull-back by f^n of a generic (in the Zariski sense) hypersurface, properly normalized, converge to the Green current…

We show that the causal-future-directed character of the energy-momentum vector of $n$-dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, $n\ge 3$, can be traced back to that of asymptotically…

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…