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Some open problems related to small divisors

  • Stefano MarmiEmail author
  • Jean-Christophe Yoccoz
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1784)

Contents.

  • 0 Introduction

  • 1 One-Dimensional Small Divisor Problems (On Holomorphic Germs and Circle Diffeomorphisms)
    • 1.1 Linearization of the quadratic polynomial. Size of Siegel disks

    • 1.2 Herman rings. Differentiable conjugacy of diffeomorphisms of the circle

    • 1.3 Gevrey classes

  • 2 Finite-Dimensional Small Divisor Problems
    • 2.1 Linearization of germs of holomorphic diffeomorphisms of \((\mathbb{C}^n, 0)\)

    • 2.2 Elliptic fixed points and KAM theory

    • 2.3 \(\mathbb{Z}^k\)-actions

    • 2.4 Diffeomorphisms of compact manifolds

  • 3 KAM Theory and Hamiltonian Systems
    • 3.1 Twist maps

    • 3.2 Euler-Lagrange flows

    • 3.3 n-body problem

  • 4 Linear Quasiperiodic Skew-Products, Spectral Theory and Hamiltonian Partial Differential Equations
    • 4.1 Reducibility of skew-products

    • 4.2 Spectral theory and integrated density of states

    • 4.3 Nonlinear Hamiltonian PDEs

  • References

Mathematics Subject Classification (2000):

37C55 37F25 37F50 37J40 37K55 47B39 34L40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di Matematica, e informaticaUniversitá di UdineUdineItaly
  3. 3.Collége de FranceParisFrance

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