Related papers: Hyperbolic development and inversion of signature

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…

We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.

We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.

In this article we review the basics of the phasor formalism in a rigorous way, highlighting the physical motivation behind it and presenting a hyperbolic counterpart of the phasor addition formula.

We present a new proof of the existence of normally hyperbolic manifolds and their whiskers for maps. Our result is not perturbative. Based on the bounds on the map and its derivative, we establish the existence of the manifold within a…

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a "hyperbolic non-percolation" property. We use this method to show that general small deformations of…

We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via…

We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…

We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented…

We present a method to construct signatures of periodic-like data. Based on topological considerations, our construction encodes information about the order and values of local extrema. Its main strength is robustness to reparametrisation…

This survey introduces to the hyperbolic unfolding correspondence that links the geometric analysis of minimal hypersurfaces with that of Gromov hyperbolic spaces. Problems caused from hypersurface singularities oftentimes become solvable…

Designing complex physical systems, including photonic structures, is typically a tedious trial-and-error process that requires extensive simulations with iterative sweeps in multi-dimensional parameter space. To circumvent this…

We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…

We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is $-I/\Delta^2$ where $I$ is the triangle's moment of inertia and $\Delta$ its…

As a simple application of special conformal transformations, we derive the electromagnetic field produced by an electric charge in hyperbolic motion. Unlike other purely algebraic derivations, here we develop a more intuitive geometrical…

We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The…

We consider the problem of when a closed hyperbolic surface admits a totally geodesic embedding into a closed hyperbolic 3-manifold, and in particular equivariant versions of such embeddings. In a previous paper we considered…

Asymptotic expansions as well as necessary and sufficient conditions are provided for the pointwise convergence of the spherical partial integrals of the associated Fourier transforms on the real hyperbolic space. The proposed method…