Hamiltonian Perturbation Theory for Ultra-Differentiable Functions.

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Title page
Introduction
1. High regularity in perturbation theory
2. Ultra-differentiable functions
3. Functions C and Ω
4. An arithmetic condition for ultra-differentiable functions
5. KAM type results
6. Hamiltonian normal forms and Nekhoroshev type results
Chapter 1. Estimates on ultra-differentiable functions
1. Majorant series and ultra-differentiable functions
2. Properties of majorant series
3. Derivatives
4. Products
5. Compositions
6. Flows
7. Inverse functions
Chapter 2. Application to KAM theory
1. Statement of the KAM theorem with parameters
2. Approximation by rational vectors
3. KAM step
4. Iterations and convergence
5. Proof of Theorem A
6. Proof of Theorem F
7. Proof of Theorem B
Chapter 3. Application to Hamiltonian normal forms and Nekhoroshev theory
1. Periodic averaging
2. Stability in the linear case: proof of Theorem H
3. Diffusion in the linear case: proof of Theorem I
4. Stability in the non-linear case: proof of Theorem J
5. Stability in the quasi-convex case: proof of Theorem K
6. Diffusion in the quasi-convex case: proof of Theorem L
7. Stability in the steep case: proof of Theorem M
Appendix A. On the moderate growth condition
Bibliography
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