相关论文: On inverse problem of dynamics

We consider the problem of recovering the Riemannian metric on a compact closed manifold from the optimal transport maps when the underlying cost function is the squared Riemann distance. We show that the metric can be uniquely determined…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…

It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…

We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by…

Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using…

We attempt to get a polynomial solution to the inverse problem, that is, to determine the form of the mechanical Hamiltonian when given the energy spectrum and transition dipole moment matrix. Our approach is to determine the potential in…

We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -\Delta + vf(x) in one dimension is known for all values of the coupling v > 0. The potential shape f(x) is assumed to be symmetric, bounded below, and…

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…

It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…

Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…

We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct a real-analytic potential by measuring the entrance and…

The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…

A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

We show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of…

Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a…

A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with…