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Generalized implicit function theorems with applications to some small divisor problems. I. (English) Zbl 0309.58006

##### MSC:
 58C15 Implicit function theorems; global Newton methods on manifolds 53B20 Local Riemannian geometry 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37C75 Stability theory for smooth dynamical systems 70F15 Celestial mechanics 70H20 Hamilton-Jacobi equations in mechanics
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