Dynamical Systems and Small Divisors

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

• Author(s): Hakan Eliasson, Sergei Kuksin,
• Publisher: Springer Science & Business Media
• Pages: 202
• ISBN_10: 3540437266
  ISBN_13: 9783540437260
  
• Language: en
• Categories: Mathematics / Mathematical Analysis , Mathematics / Functional Analysis , Mathematics / Differential Equations / General , Mathematics / Linear & Nonlinear Programming ,

Description:... Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.