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Methods of complex analysis in classical perturbation theory
by Antonio Giorgilli

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Contents:

1. Overview: 3
2. Lie series and Lie transforms: 4
   • Formal definitions: 4
   • Cauchy estimates: 8
   • Analytic framework: 9
   • Weighted Fourier norms: 10
   • Generalized Cauchy estimates: 11
   • Analyticity of Lie series and of Lie transform: 14
3. Normal form theory: 18
   • Formal scheme: 19
   • Quantitative estimates on the generating sequence: 22
   • Local estimates: 26
4. Exponential stability: 27
   • Geography of resonances: 28
   • Global estimates: 30
   • The exponential estimate: 31
5. References: 32

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Chaos and diffusion in Hamiltonian systems, D. Benest and C. Froeschlé eds., Editions Frontières (1995)

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