# Books written by Jean-Christophe Yoccoz.

"Proving stability properties – dynamic stability, such as that sought for the solar system, or structural stability, meaning persistence under parameter changes of the global properties of the system." Fields Medal recipient of 1994.

## From Number Theory to Physics

The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoretical Physics. The first part is mathematically oriented; it deals mostly with elliptic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems.

## Dynamical Systems and Small Divisors

Lectures given at the C.I.M.E. Summer School held in Cetraro Italy, June 13-20, 1998

## Dynamical Systems

Michael Robert Herman had a profound impact on the theory of dynamical systems over the last 30 years. His seminar at the École Polytechnique had major worldwide influence and was the main vector in the development of the theory of dynamical systems in France. His interests covered most aspects of the subject though closest to his heart were the so-called small divisors problems, in particular those related to the stability of quasiperiodic motions.