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Analytic linearization of circle diffeomorphisms

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

Contents.

  • 1 Introduction

  • 2 Arithmetics
    • 2.1 Introduction

    • 2.2 Continued Fractions

    • 2.3 Diophantine Conditions

    • 2.4 Brjuno function and condition \(\mathcal{B}\)

    • 2.5 Condition \(\mathcal{H}\)

    • 2.6 \(\mathbb{Z}^{2}\)-actions by translations and continued fractions

  • 3 The \(\mathcal{C}^r\) theory for \(r \geq 0\)
    • 3.1 The \(\mathcal{C}^0\) theory

    • 3.2 Equicontinuity and topological conjugacy

    • 3.3 The Denjoy theory.

    • 3.4 Denjoy’s counter-examples

    • 3.5 The Schwarzian derivative

    • 3.6 Partial renormalization

  • 4 Analytic case
    • 4.1 A linearization criterion

    • 4.2 Local Theorem 1.2: big strips

    • 4.3 Local Theorem 1.3: small strips

    • 4.4 Global Theorem: complex Denjoy estimates

    • 4.5 Global Theorem: proof of linearization

    • 4.6 Global Theorem: Construction of nonlinearizable diffeomorphisms

  • 5 Appendix: Estimates of moduli of annular domains
    • 5.1 Dirichlet integrals

    • 5.2 First kind of moduli estimates

    • 5.3 Second kind of moduli estimates

  • 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.Collége de FranceParisFrance

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