The real trouble with this world of ours
is not that it is an unreasonable world,
nor even that it is a reasonable one.
The commonest kind of trouble is that
it is nearly reasonable, but not quite.
Life is not an illogicality;
yet it is a trap for logicians.
It looks just a little
more mathematical and regular than it is;
its exactitude is obvious,
but its inexactitude is hidden;
its wildness lies in wait.

(G. K. Chesterton)

Perturbation methods in Celestial Mechanics


The lectures are concerned with the old-standing problem of stability of a planetary system. The aim is to present some relevant phases of the development of our knowledge on this subject.
Specific topics will be:
  1. A brief historical account of the origin of the problem of stability, from Kepler to the end of the XIX century, including the theorem of Poincaré on non integrability.
  2. The theorem of Kolmogorov on persistence of invariant tori.
  3. The problem of stability of an equilibrium and of an invariant torus, through the theory of Poincaré and Birkhoff.
  4. The long time stability, with the general formulation of the theorem of Nekhoroshev on exponential stability and the concept of superexponential stability.
  5. A short discussion of some recent results based on computer assisted methods.

Documentation on line:

Here you can find a copy of the slides that will be shown during the lectures.
Actually, the lectures will use only part of the material included here. However, I hope that participants will appreciate the extra information.
The slides are written in CTL (Common Technical Language). It has some resemblance with english, so I hope it will be readable.
The documentation is subject to changes. Constructive criticism is appreciated.

  1. Documentation in size A4, portrait format, 10 point font, with space for personal notes on every page.
  2. Documentation in size A4, landscape format, 12 point font.
  3. A preliminary list of references.

Fairy tales do not tell children the dragons exist.
Children already know that dragons exist.
Fairy tales tell children the dragons can be killed.
(G.K. Chesterton)

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