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Surgery on Herman rings of the standard Blaschke family
Northwest University, School of Mathematics, Xi'an Shaanxi 710127, China |
$B_{\alpha ,a}$ |
${B_{\alpha ,a}}(z) = {e^{2\pi {\rm{\mathbf{i}}}\alpha }}{z^{d + 1}}{(\frac{{z - a}}{{1 - az}})^d}.$ |
$B_{\alpha ,a}|_{S^1}$ |
$B_{\alpha ,a}$ |
$θ$ |
$(\alpha ,a)$ |
$B_{\alpha ,a}|_{S^1}$ |
$θ$ |
$T_d(θ)$ |
$θ$ |
$a=M(θ)$ |
$∞$ |
$M(θ)≥q 2d+1$ |
$θ ∈ \mathcal {B}\setminus\mathcal {H}$ |
$M(θ)$ |
$2d+1$ |
References:
[1] |
L. Ahlfors,
Lectures on Quasiconformal Mappings 2$^{nd}$ edition, University Lecture Series, 38 2006.
doi: 10.1090/ulect/038. |
[2] |
V. Arnold,
Small denominators I: On the mapping of a circle into itself, Nauk. Math., Series, 25 (1961), 21-96.
|
[3] |
H. F. Chu,
On the Blaschke circle diffeomorphisms, Proceedings of the American Mathematical Society, 143 (2015), 1169-1182.
doi: 10.1090/S0002-9939-2014-12359-8. |
[4] |
N. Fagella and L. Geyer,
Surgery on Herman rings of the complex standard family, Ergodic Theory and Dynamical Systems, 23 (2003), 493-508.
doi: 10.1017/S0143385702001323. |
[5] |
L. Geyer,
Siegel disks, Herman rings and Arnold family, Trans. Amer. Math. Soc., 353 (2001), 3661-3683.
doi: 10.1090/S0002-9947-01-02662-9. |
[6] |
C. Henriksen, Holomorphic Dynamics and Herman Rings Master's thesis, Technical University of Denmark, 1997. Google Scholar |
[7] |
M. Herman,
Sur les conjugaison différentiable des difféomorphismes du cercle á des rotations, Publ. Math. IHES., 49 (1979), 5-233.
|
[8] |
M. Herman, Conjugaison quasi-symmétrique des difféomorphismes du cercle á des rotations et applications aux disques singuliers de siegel I, unpublished manuscript. Google Scholar |
[9] |
O. Lehto and K. Virtanen, Quasiconformal Mappings in the Plane Springer-Verlag, 1973. |
[10] |
W. de Melo and S. van Strien, One-Dimensional Dynamics Springer-Verlag, 1993.
doi: 10.1007/978-3-642-78043-1. |
[11] |
J. Milnor, Dynamics in One Complex Variable ntroductory Lectures, 2000.
doi: 10.1007/978-3-663-08092-3. |
[12] |
E. Risler,
Linéarisation des perturbations holomorphes des rotations et applications, Mémoires de la Société Mathématique de France, 77 (1999), 1-102.
|
[13] |
M. Shishikura,
On the quasiconformal surgery of rational functions, Ann. Sci. École Norm., 20 (1987), 1-29.
doi: 10.24033/asens.1522. |
[14] |
J. C. Yoccoz,
Analytic linearization of circle diffeomorphisms in Dynamical Systems and Small Divisors (Lecture Notes in Mathematics), Springer, Berlin, 1784 (2002), 125-173.
doi: 10.1007/978-3-540-47928-4_3. |
show all references
References:
[1] |
L. Ahlfors,
Lectures on Quasiconformal Mappings 2$^{nd}$ edition, University Lecture Series, 38 2006.
doi: 10.1090/ulect/038. |
[2] |
V. Arnold,
Small denominators I: On the mapping of a circle into itself, Nauk. Math., Series, 25 (1961), 21-96.
|
[3] |
H. F. Chu,
On the Blaschke circle diffeomorphisms, Proceedings of the American Mathematical Society, 143 (2015), 1169-1182.
doi: 10.1090/S0002-9939-2014-12359-8. |
[4] |
N. Fagella and L. Geyer,
Surgery on Herman rings of the complex standard family, Ergodic Theory and Dynamical Systems, 23 (2003), 493-508.
doi: 10.1017/S0143385702001323. |
[5] |
L. Geyer,
Siegel disks, Herman rings and Arnold family, Trans. Amer. Math. Soc., 353 (2001), 3661-3683.
doi: 10.1090/S0002-9947-01-02662-9. |
[6] |
C. Henriksen, Holomorphic Dynamics and Herman Rings Master's thesis, Technical University of Denmark, 1997. Google Scholar |
[7] |
M. Herman,
Sur les conjugaison différentiable des difféomorphismes du cercle á des rotations, Publ. Math. IHES., 49 (1979), 5-233.
|
[8] |
M. Herman, Conjugaison quasi-symmétrique des difféomorphismes du cercle á des rotations et applications aux disques singuliers de siegel I, unpublished manuscript. Google Scholar |
[9] |
O. Lehto and K. Virtanen, Quasiconformal Mappings in the Plane Springer-Verlag, 1973. |
[10] |
W. de Melo and S. van Strien, One-Dimensional Dynamics Springer-Verlag, 1993.
doi: 10.1007/978-3-642-78043-1. |
[11] |
J. Milnor, Dynamics in One Complex Variable ntroductory Lectures, 2000.
doi: 10.1007/978-3-663-08092-3. |
[12] |
E. Risler,
Linéarisation des perturbations holomorphes des rotations et applications, Mémoires de la Société Mathématique de France, 77 (1999), 1-102.
|
[13] |
M. Shishikura,
On the quasiconformal surgery of rational functions, Ann. Sci. École Norm., 20 (1987), 1-29.
doi: 10.24033/asens.1522. |
[14] |
J. C. Yoccoz,
Analytic linearization of circle diffeomorphisms in Dynamical Systems and Small Divisors (Lecture Notes in Mathematics), Springer, Berlin, 1784 (2002), 125-173.
doi: 10.1007/978-3-540-47928-4_3. |
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