KAM tori for higher dimensional beam equations with constant potentials
KAM tori for higher dimensional beam equations with constant potentials
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DOI：
10.1088/0951-7715/19/10/007
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发表时间：
2006-09
期刊：
影响因子：
1.7
通讯作者：
J. Geng;J. You
中科院分区：
文献类型：
--
作者：
J. Geng;J. You
本文考虑具有周期边界条件的高维非线性梁方程，其中非线性项f(U)是u=0附近的实解析函数，f(0)=f‘(0)=0，σ是区间上的实参数。证明了对于位于有限区间内的‘大多数’正参数σ，上述方程存在一族小幅度的、线性稳定的准周期解，对应于相应的无限维动力系统的有限维不变环面的康托尔族.这个证明是基于一个无限维Kam定理，该定理是由(耿爽和游2006)修正的。数学课。太棒了。262 343-72)和徐静等人1996年的科学中国爵士。A 39372-83,383-94)，具有较弱的非简并条件。
In this paper, we consider the higher dimensional nonlinear beam equations with periodic boundary conditions, where the nonlinearity f(u) is a real–analytic function near u = 0 with f(0) = f′(0) = 0 and σ is a real parameter in an interval . It is proved that for ‘most’ positive parameters σ lying in the finite interval , the above equations admit a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to a Cantor family of finite dimensional invariant tori of an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem, modified from (Geng and You 2006 Commun. Math. Phys. 262 343–72) and (Xu J et al 1996 Sci. China Ser. A 39 372–83, 383–94) with weaker non-degeneracy conditions.