The stability of equilibrium solutions of periodic Hamiltonian systems in the case of degeneracy

2017/05/30 by Nina Xue, Xiong Li, Xue, Nina +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1705.10484

22 pages

arxiv created 2017/05/30 · arxiv updated 2017/05/31

Abstract

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have zero real part, and the high order terms must be considered to solve the stability problem. For almost all degenerate cases, sufficient conditions for the stability and instability are obtained.

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