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6 papers · 1 filter
On Convergence to Equilibrium Distribution, II. The Wave Equation in Odd Dimensions, with Mixing
T. V. Dudnikova, A. I. Komech, N. E. Ratanov +1
The paper considers the wave equation, with constant or variable coefficients in , with odd . We study the asymptotics of the distribution of the random soluti…
Two-body quantum mechanical problem on spheres
Alexey V. Shchepetilov
The quantum mechanical two-body problem with a central interaction on the sphere is considered. Using recent results in representation theory an ordinary differential…
Spectra of Sol-manifolds: arithmetic and quantum monodromy
A. V. Bolsinov, H. R. Dullin, A. P. Veselov
The spectral problem of three-dimensional manifolds M_A admitting Sol-geometry in Thurston's sense is investigated. Topologically M_A are torus bundles over a circle with a unimodu…
Coupling of eigenvalues of complex matrices at diabolic and exceptional points
A. A. Mailybaev, O. N. Kirillov, A. P. Seyranian
The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are di…
Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces
Yuri N. Fedorov, Bozidar Jovanovic
We consider a class of dynamical systems on a Lie group with a left-invariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a…
Spectral portraits of the Orr--Sommerfeld operator with large Reynolds numbers
A. A. Shkalikov
A model problem of the form -iεy''+q(x)y=λy, y(-1)=y(1)=0, is associated with well-known in hydrodynamics Orr--Sommerfeld operator. Here (λ) is the spectral parameter, (ε) is the s…