A Nash-moser Theorem with Near-minimal Hypothesis
نویسنده
چکیده
A proof of a Nash-Moser type inverse function theorem is given under substantially weaker hypothesis than previously known. Our method is associated with continuous Newton’s method rather than the more conventional Newton’s method.
منابع مشابه
Integrated Form of Continuous Newton’s Method
An integrated form of continuous Newton’s method is defined. Under rather minimal conditions the method is shown to lead to a zero of the given function. The result is applied to recover a recent Nash-Moser type inverse function theorem.
متن کاملA New Proof of the Newlander–Nirenberg Theorem
The proof of the Newlander-Nirenberg theorem is given by integral formula methods and a functional analytic argument on continuous linear operators with small operator norms. No Nash-Moser iteration is needed. These formulae might be also useful for other applications.
متن کاملA canonical small divisor problem for the Nash-Moser method
In this note we prove a general elementary small divisor theorem for Hs norms of N ×N matrices that provides a potentially useful estimate for expunging resonances in Nash-Moser Newton Iterations. The theorem requires compatibility conditions on the approximating matrices, and we investigate how the theorem can fail when the compatibility conditions are violated. This investigation suggests tha...
متن کاملA Local Inversion Principle of the Nash-Moser Type
We prove an inverse function theorem of the Nash–Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824–1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinit...
متن کاملRelative Nonlinear Normal Modes of Hamiltonian Systems
We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we significantly improve a result proved earlier jointly with Tokieda: we remove a techni...
متن کامل