The real trouble with this world of oursis 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) |

Specific topics will be:

- 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.
- The theorem of Kolmogorov on persistence of invariant tori.
- The problem of stability of an equilibrium and of an invariant torus, through the theory of Poincaré and Birkhoff.
- The long time stability, with the general formulation of the theorem of Nekhoroshev on exponential stability and the concept of superexponential stability.
- A short discussion of some recent results based on computer assisted methods.

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

The documentation is subject to changes. Constructive criticism is appreciated.

- Documentation in size A4, portrait format, 10 point font, with space for personal notes on every page.
- Documentation in size A4, landscape format, 12 point font.
- 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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