Related papers: Symplectic approach to global stability

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…

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.…

We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…

Our aim is to give a friendly introduction for students to systolic inequalities. We will stress the relationships between the classical formulation for Riemannian metrics and more recent developments related to symplectic measurements and…

In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability…

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…

Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable…

We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…

In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…

In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept of consistent implicit maps, to generalize the symplecticity…

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete…

We prove the semi-global controllability and stabilization of the $(1+1)$-dimensional wave maps equation with spatial domain $\mathbb{S}^1$ and target $\mathbb{S}^k$. First we show that damping stabilizes the system when the energy is…

In this paper the homology stability for symplectic groups over a ring with finite stable rank is established. First we develop a `nerve theorem' on the homotopy type of a poset in terms of a cover by subposets, where the cover is itself…

This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality.…

We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non trivial way. These systems depend on a parameter t $\in$ [0, 1] and exhibit different behaviors…

We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…

We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize…

Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…

We prove packing stability for any closed symplectic manifold with rational cohomology class. This will rely on a general symplectic embedding result for ellipsoids which assumes only that there is no volume obstruction and that the domain…