A proof of the Palamodov's total instability conjecture

2021/08/12 by Juan Manuel Burgos, Burgos, J. M.
Physics and Astronomy · #Astro and Planetary Science #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2108.05829

openalex publication_date 2021/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give for the first time a detailed proof of the Palamodov's total instability conjecture in Lagrangian dynamics. This proves an older related Lyapunov instability conjecture posed by Lyapunov and Arnold and reduces the Lagrange-Dirichlet converse problem in the class of real analytic potentials to the Lyapunov instability of non strict minimum critical points. It also proves the instability of charged rigid bodies under the presence of an external electrostatic field.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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