相关论文: On the Jacobi-Metric Stability Criterion

The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…

We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from…

Consider a $1$-dimensional centered Gaussian process $W$ with $\alpha$-H\"older continuous paths on the compact intervals of $\mathbb R_+$ ($\alpha\in ]0,1[$) and $W_0 = 0$, and $X$ the local solution in rough paths sense of Jacobi's…

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…

We introduce an exactly solvable example of timelike geodesic motion and geodesic deviation in the background geometry of a well-known two-dimensional black hole spacetime. The effective potential for geodesic motion turns out to be either…

We argue by way of examples that, as a nonlinear integral equation, the gap equation can and does possess many physically distinct solutions for the dressed-quark propagator. The examples are drawn from a class that is successful in…

We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the…

The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this…

We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to…

We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…

In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…

We establish the stability of metric viscosity solutions to first-order Hamilton--Jacobi equations under Gromov--Hausdorff convergence. Our proof combines a characterization of metric viscosity solutions via quadratic distance functions…

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…

One method of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work the Hamilton-Jacobi…

Here we propose a new method to study gravitational stability of the solutions to the Einstein equations. This method uses the canonical superenergy density and it is different from approaches already used (Lyapunov's stability, dynamical…

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces…

The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…

We analyze the stability of circular geodesics for timelike as well as null geodesics of the Kerr BH spacetime with rotation parameter on the equatorial plane by Lyapunov stability analysis. Also, we verify the results of stability by…

In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…

An analytical solution to the nonlinear differential equation describing the equation of motion of a particle moving in an unforced physical system with linear damping, governed by a cubic potential well, is presented in terms of the Jacobi…