McGehee blowup for Lagrangian systems and instability of equilibria

2025/06/23 by Juan Manuel Burgos, Burgos, J. M.
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Navier-Stokes equation solutions #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2506.19135

Abstract

We prove that total instability is a generic phenomenon in the real analytic class of electromagnetic Lagrangian systems under a weak magnetism hypothesis. The main object in the proof is an adaptation of the McGehee blowup for these systems. Together with this result, new criteria for total instability are introduced for both generic and non-generic cases.

Citations

• Compactification of the energy surfaces for n bodies

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