Generalized implicit function theorems with applications to some small divisor problems, I
Generalized implicit function theorems with applications to some small divisor problems, I
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DOI：
10.1002/cpa.3160280104
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发表时间：
1976
影响因子：
3
通讯作者：
E. Zehnder
中科院分区：
文献类型：
--
作者：
E. Zehnder
答:目标。标准存在性定理无法解决的各种非线性问题导致了新的和巧妙的方法和技术，这些方法和技术使得J.纳什（J. Nash）的等尺度嵌入问题和AN . Kolmogorov, VI . Arnol'd和J. Moser （J. Moser）的所谓小因子困难的哈密顿系统的稳定性问题得以解决[141]。随后，隐含的思想被不同的作者抽象为隐函数定理，J. Schwartz [17],[18]， H. Jacobowitz [2]， L. Nirenberg [3]， F. Sergeraert[20]，以及最近的R. S. Hamilton[27]。然而，上述小因子问题包含一个额外的困难，这是任何这些抽象方法都无法解决的。本文的目的是表述和证明一个涵盖这些定理的广义隐函数定理。事实证明，抽象设置只需要对以前的方法进行相当简单的修改；然而，它是zyxwvutsrqp
A. Aim. Various nonlinear problems, not accessible to standard existence theorems led to new and ingenious methods and techniques which allowed the solution of the isometric imbedding problem by J. Nash [19] and stability problems of Hamiltonian systems which are related to the so-called difficulty of small divisors by AN Kolmogorov, VI Arnol'd and J. Moser [4]-[141. Subsequently the underlying ideas were abstracted as implicit function theorms by various authors, J. Schwartz [17],[18], H. Jacobowitz [2], L. Nirenberg [3], F. Sergeraert [20], and more recently R. S. Hamilton [27]. However, the above small divisor problems contain an additional difficulty which could not be tackled by any of these abstract approaches. It is the aim of this paper to formulate and prove a generalized implicit function theorem that does cover these theorems. It turns out that the abstract setup requires only a fairly easy modification of previous methods; however it is zyxwvutsrqp