Book contents
- Frontmatter
- Dedication
- Contents
- Apology
- Plan of the Book
- Part IFrom Ancient Astronomy to Newton
- Part IIFrom Newton to Poincaré
- Part IIIModern Celestial Mechanics
- 9A Toolbox of Perturbation Methods
- 10Computer-Assisted Methods for KAM Theory
- 11Rotational Dynamics of Celestial Bodies
- 12Stability of Planetary Systems
- Appendix AAnalytical Tools
- Appendix BIndexing Functions
- Appendix CValidated Numerics in CAP
- Appendix DBenchmarking CAP with a Simple Model
- References
- Index
9 - A Toolbox of Perturbation Methods
from Part III - Modern Celestial Mechanics
Published online by Cambridge University Press: 25 June 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Apology
- Plan of the Book
- Part IFrom Ancient Astronomy to Newton
- Part IIFrom Newton to Poincaré
- Part IIIModern Celestial Mechanics
- 9A Toolbox of Perturbation Methods
- 10Computer-Assisted Methods for KAM Theory
- 11Rotational Dynamics of Celestial Bodies
- 12Stability of Planetary Systems
- Appendix AAnalytical Tools
- Appendix BIndexing Functions
- Appendix CValidated Numerics in CAP
- Appendix DBenchmarking CAP with a Simple Model
- References
- Index
Summary
So far we have dealt with classical analytic methods, concerning in particular the system of three bodies. Beginning with this chapter we make a jump in time to the second half of the twentieth century. The aim is to illustrate some recent developments. Reference is made in particular to the two main theorems proved after 1950: Kolmogorov’s theorem on persistence of invariant tori [127], and Nekhoroshev’s theorem on exponential stability [195][196].
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- Celestial MechanicsClassical and Modern Methods, pp. 269 - 296Publisher: Cambridge University PressPrint publication year: 2026
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