Related papers: On a matrix-valued PDE characterizing a contractio…
Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…
We show that the monodromy of a spherical conical metric is reducible if and only if it has a real-valued eigenfunction with eigenvalue 2 in the holomorphic extension of the associated Laplace--Beltrami operator. Such an eigenfunction…
We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…
A metric representing a slowly rotating object with quadrupole moment is obtained using a perturbation method to include rotation into the weak limit of the Erez-Rosen metric. This metric is intended to tackle relativistic astrometry and…
We study the existence of a global periodic attractor for the reduced dynamics of a discrete toy model for rectilinear crawling locomotion, corresponding to a limit cycle in the shape and velocity variables. The body of the crawler consists…
We define a formal Riemannian metric on a given conformal class of metrics on a closed Riemann surface. We show interesting formal properties for this metric, in particular the curvature is nonpositive and the Liouville energy is…
This paper addresses the trajectory-tracking problem for a class of electromechanical systems. To this end, the dynamics of the plants are modeled in the so-called port-Hamiltonian framework. Then, the notion of contraction is exploited to…
We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then we investigate the asymptotic behavior of the displacement solution as the Robin condition…
During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these…
We study scattering rigidity in Lorentzian geometry: recovery of a Lorentzian metric from the scattering relation $\mathcal{S}^\sharp$ known on a lateral boundary. We show that, under a non-conjugacy assumption, every defining function…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
In this article we introduce a diffeomorphism-invariant Riemannian metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We consider the steady Swift - Hohenberg partial differential equation. It is a one-parameter family of PDE on the plane, modeling for example Rayleigh - B\'enard convection. For values of the parameter near its critical value, we look for…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
Frozen orbits are always important foci of orbit design because of their valuable characteristics that their eccentricity and argument of pericentre remain constant on average. This study investigates quasi-circular frozen orbits and…