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We prove the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings, and explicitly construct the unstable mode of the inner catenoid, by studying the spectrum of an exactly solvable one-dimensional Schrodinger operator with an asymmetric Darboux-Poschl-Teller potential.
A Poisson realization of the simple real Lie algebra $mathfrak {so}^*(4n)$ on the phase space of each $mathrm {Sp}(1)$-Kepler problem is exhibited. As a consequence one obtains the Laplace-Runge-Lenz vector for each classical $mathrm{Sp}(1)$-Kepler p
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
In this paper we study the convex cone of not necessarily smooth measures satisfying the classical KMS condition within the context of Poisson geometry. We discuss the general properties of KMS measures and its relation with the underlying Poisson ge
In this paper, we study the Dirac equation for an electron constrained to move on a catenoid surface. We decoupled the two components of the spinor and obtained two Klein-Gordon-like equations. Analytical solutions were obtained using supersymmetric
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle.