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We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.
We are interested in the phenomenon of the essential spectrum instability for a class of unbounded (block) Jacobi matrices. We give a series of sufficient conditions for the matrices from certain classes to have a discrete spectrum on a half-axis of
We perform the study of the stability of the Lorenz system by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. The Lorenz model plays an important role for understanding hydrodynamic instabilities and the nature of the t
We prove that a perfect four-feet square table, posed in a continuous irregular ground with a local slope of at most 15 degrees can be put in equilibrium on the ground by a rotation of less than 90 degrees. We also discuss the case of non-square tabl
The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e., conditions under which it holds sup_{t in R} | (psi(t),H(t) psi(t)) |<infty w
We propose two ways for determining the Greens matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from the Jacobi-