اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAnalytic linearization of conformal maps of the annulus
108
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider holomorphic maps defined in an annulus around $mathbb R/mathbb Z$ in $mathbb C/mathbb Z$. E. Risler proved that in a generic analytic family of such maps $f_zeta$ that contains a Brjuno rotation $f_0(z)=z+alpha$, all maps that are conjugate to this rotation form a codimension-1 analytic submanifold near $f_0$. In this paper, we obtain the Rislers result as a corollary of the following construction. We introduce a renormalization operator on the space of univalent maps in a neighborhood of $mathbb R/mathbb Z$. We prove that this operator is hyperbolic, with one unstable direction corresponding to translations. We further use a holomorphic motions argument and Yoccozs theorem to show that its stable foliation consists of diffeomorphisms that are conjugate to rotations.
قيم البحث
اقرأ أيضاً
One considers a system on $mathbb{C}^2$ close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic linearization of the
system around the invariant curve is bounded from below by $exp(-frac{2}{d}B(dalpha)-C)$, where $Cgeq 0$ does not depend on $alpha$, $din mathbb{N}^*$ and $alpha$ is the frequency of the linear part. For a class of trigonometric polynomials, it is also bounded from above by a similar function. The error function is non decreasing with respect to the smallest coefficient of the trigonometric polynomial.
Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes identified by EDMD correspond to those of compact Perron-Frobenius an
d Koopman operators defined on suitable Hardy-Hilbert spaces when the method is applied to classes of analytic maps. Our findings elucidate the interpretation of the spectra obtained by EDMD for complex dynamical systems. We illustrate our results by numerical simulations for analytic maps.
We show that for any $lambda in mathbb{C}$ with $|lambda|<1$ there exists an analytic expanding circle map such that the eigenvalues of the associated transfer operator (acting on holomorphic functions) are precisely the nonnegative powers of $lambda
$ and $bar{lambda}$. As a consequence we obtain a counterexample to a variant of a conjecture of Mayer on the reality of spectra of transfer operators.
We find the exact radius of linearization disks at indifferent fixed points of quadratic maps in $mathbb{C}_p$. We also show that the radius is invariant under power series perturbations. Localizing all periodic orbits of these quadratic-like maps we
then show that periodic points are not the only obstruction for linearization. In so doing, we provide the first known examples in the dynamics of polynomials over $mathbb{C}_p$ where the boundary of the linearization disk does not contain any periodic point.
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries from another work of the authors.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
