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On types of stability in Hamiltonian systems
Article ID: 2269
Vol 1, Issue 1, 2023
DOI: https://doi.org/10.54517/mss.v1i1.2269
Vol 1, Issue 1, 2023
Received: 3 August 2023; Accepted: 21 October 2023; Available online: 3 November 2023; Issue release: 15 November 2023
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Abstract
We consider conditions of three types of stability: Lyapunov, formal and weak of a stationary solution, and of a periodic solution in a Hamiltonian system with a finite number of degrees of freedom. The conditions contain restrictions on the order of resonances and some inequalities for initial coefficients of the normal forms of the Hamiltonian functions. We show that the number-theoretical analysis of frequencies can help in proof of stability. We also estimate the orders of solutions’ divergence from the stationary or the periodic ones under lack of formal stability.
Keywords
stationary solution; periodic solution; normal form; formal stability; weak stability
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Cairo University, Egypt
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