Related papers: On hyperbolic fixed points in ultrametric dynamics

For a noncompact complex hyperbolic space form of finite volume $X=\mathbb{B}^n/\Gamma$, we consider the problem of producing symmetric differentials vanishing at infinity on the Mumford compactification $\overline{X}$ of $X$ similar to the…

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.

We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e.\ on compact time sets. For linear finite-time processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is…

We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension greater than 2, only finitely many hyperbolic n-manifolds are total…

Let M be a compact hyperbolic manifold with totally geodesic boundary. If the injectivity radius of the boundary is larger than an explicit function of the normal injectivity radius of the boundary, we show that there is a negatively curved…

A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…

We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…

We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…

We establish two results under which the topology of a hyperbolic set constrains ambient dynamics. First if a set is a compact, transitive, expanding hyperbolic attractor of codimension 1 for some diffeomorphism, then it is a union of…

We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann loss', a new…

We study subgroups of ${\rm PU}(2,1)$ generated by two non-commuting unipotent maps $A$ and $B$ whose product $AB$ is also unipotent. We call $\mathcal{U}$ the set of conjugacy classes of such groups. We provide a set of coordinates on…

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…

Consider a stationary Poisson process in a $d$-dimensional hyperbolic space. For $R>0$ define the point process $\xi_R^{(k)}$ of exceedance heights over a suitable threshold of the hyperbolic volumes of $k$th nearest neighbour balls centred…

In this paper, we prove $L^p$ ($p > 1$) dimension free bounds for the centered Hardy-Littlewood maximal function on real or complex hyperbolic spaces.

We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…

Following Santal\'{o}'s approach, we prove several characterizations of a disc among bodies of constant width, constant projections lengths, or constant section lengths on given families of geodesics.

We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.

In this paper, we prove restriction estimates for hyperbolic paraboloids in dimensions $n>=5$ by the polynomial partitioning method.

We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…

Let U be the open unit disc in C and let B be the open unit ball in C^2. We prove that every discrete subset of B is contained in the range f(U) of a complete, proper holomorphic embedding f:U-->B. Here the completeness of f means that for…