Generic IllPosedness for Wave Equation of Power Type on Three-Dimensional Torus
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DOI: 10.1093/imrn/rnaa068
Abstract: In the present work, we show that the wave equation in three-dimensional torus of power-type nonlinearity is ill posed around any (relatively) regular dynamics in the super-critical regime. In the cubic case, we can even… read more here.
Keywords: three dimensional; dimensional torus; wave equation; power type ... See more keywords
Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators
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DOI: 10.1115/1.4048025
Abstract: Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic… read more here.
Keywords: two zero; lyapunov exponents; dimensional torus; three dimensional ... See more keywords
Some Remarks on High Degree Polynomial Integrals of the Magnetic Geodesic Flow on the Two-Dimensional Torus
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DOI: 10.1134/s0037446621040017
Abstract: We study the magnetic geodesic flow on the two-dimensional torus which admits an additional high degree first integral polynomial in momenta and is independent of the energy integral. In an earlier work by the first two authors, it… read more here.
Keywords: magnetic geodesic; geodesic flow; high degree; two dimensional ... See more keywords