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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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