The linearization of periodic Hamiltonian systems with one degree of freedom under the Diophantine condition

2017/05/24 by Nina Xue, Xiong Li, Xue, Nina +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1705.08766

arxiv created 2017/05/24 · arxiv updated 2017/05/25

Abstract

In this paper we are concerned with the periodic Hamiltonian system with one degree of freedom, where the origin is a trivial solution. We assume that the corresponding linearized system at the origin is elliptic, and the characteristic exponents of the linearized system are ± iω with ω be a Diophantine number, moreover if the system is formally linearizable, then it is analytically linearizable. As a result, the origin is always stable in the sense of Liapunov in this case.

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