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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yoccoz, JC. (2002). Analytic linearization of circle diffeomorphisms. In: Dynamical Systems and Small Divisors. Lecture Notes in Mathematics, vol 1784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47928-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-47928-4_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43726-0
Online ISBN: 978-3-540-47928-4
eBook Packages: Springer Book Archive