Invariant tori for semilinear reversible systems

✍ Scribed by Xiong Li

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 228 KB
• Volume: 56
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2003.09.004

✦ Synopsis

In this paper we consider the problem of the boundedness of all solutions for the oscillator

where ! ¿ 0 and ! ∈ N , g(x) is bounded and p(t) = p(t + 2 ). Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible maps. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.