Related papers: A generalized global Hartman-Grobman theorem for a…

We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the ``sample and hold''…

Universality theorems (in the sense of N. Mn\"{e}v) claim that the realization space of a combinatorial object (a point configuration, a hyperplane arrangement, a convex polytope, etc.) can be arbitrarily complicated. In the paper, we prove…

We study the asymptotic behavior of solutions to the Dirichlet problem for Hamilton-Jacobi equations with large drift terms, where the drift terms are given by the Hamiltonian vector fields of Hamiltonian $H$. This is an attempt to…

Integrable Hamiltonian systems on almost-symplectic manifolds have recently drawn some attention. Under suitable properties, they have a structure analogous to those of standard symplectic-Hamiltonian completely integrable systems. Here we…

This paper is devoted to the analysis of global stability of the chemostat system with a perturbation term representing any type of exchange between species. This conversion term depends on species and substrate concentrations but also on a…

We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…

The aim of this paper is to discuss the theory of Newtonian and relativistic polytropes with generalized polytropic equation of state. For this purpose, we formulated the general framework to discuss the physical properties of polytrops…

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable…

We consider the wave equation on asymptotically Minkowski spacetimes and the Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases we show that the extreme difference of propagators (i.e. retarded propagator minus…

In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 437-478 -- see also arXiv:1804.11290), the same authors have studied viscous…

Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…

In this paper we extend existing results for generalized solitons, called $q$-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field $X$ and curvature conditions on $M$, we…

We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of…

In this paper, we provide a novel solution to an open problem on the global uniform stability of switched nonlinear systems. Our results are based on the Koopman operator approach and, to our knowledge, this is the first theoretical…

We develop a theory of semialgebra Grassmann triples via Hasse-Schmidt derivations, which formally generalizes results such as the Cayley-Hamilton theorem in linear algebra, thereby providing a unified approach to classical linear algebra…

The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…

We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the…

We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a non symplectic force is added, so that the phase space volume is not preserved. The vector field depends upon two parameters,…

We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds $T \times G$, where $G$ is further assumed…

A classical result in Differential Geometry states that the flows of two smooth vector fields commute if and only if their Lie Bracket vanishes. In this work, we extend this result to a more general setting where one of the vector fields is…