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pro vyhledávání: '"Aspenberg, P."'
In this paper we study perturbations of complex unicritical polynomials satisfying the Collet-Eckmann condition. We show that Collet-Eckmann parameters are Lebesgue density points of the complement of the Mandelbrot set (i.e. the connectedness locus)
Externí odkaz:
http://arxiv.org/abs/2402.19256
Publikováno v:
Ergodic Theory and Dynamical Systems 2024
Consider the quadratic family $T_a(x) = a x (1 - x)$, for $x \in [0, 1]$ and mixing Collet--Eckmann (CE) parameters $a \in (2,4)$. For bounded $\varphi$, set $\tilde \varphi_{a} := \varphi - \int \varphi \, d\mu_a$, with $\mu_a$ the unique acim of $T
Externí odkaz:
http://arxiv.org/abs/2212.12202
Autor:
Aspenberg, Magnus, Cui, Weiwei
Publikováno v:
Comm. Math. Phys. 405 (2024), no. 2, Paper No. 55
We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (in the sense of Eremenko and Lyubich). We show that every Misiurewicz e
Externí odkaz:
http://arxiv.org/abs/2209.00385
Publikováno v:
Proc. Lond. Math. Soc. (3) 128 (2024), no. 1, Paper No. e12574, 32 pp
In this paper we study rational Collet-Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families where the orders of the critical points are fixed, we prove that such maps
Externí odkaz:
http://arxiv.org/abs/2207.14046
Autor:
Aspenberg, Magnus, Cui, Weiwei
Publikováno v:
J. Anal. Math. 153 (2024), no. 2, 759-775
We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which comple
Externí odkaz:
http://arxiv.org/abs/2206.11093
Autor:
Aspenberg, Magnus
In this paper we study perturbations of rational Collet-Eckmann maps for which the Julia set is the whole sphere, and for which the critical set is allowed to be slowly recurrent. We show that any such map is a Lebesgue density point of Collet-Eckman
Externí odkaz:
http://arxiv.org/abs/2103.14432
Autor:
Aspenberg, Magnus, Cui, Weiwei
Publikováno v:
Ergodic Theory Dynam. Systems 43 (2023), no. 5, 1471-1491
A function which is transcendental and meromorphic in the plane has at least two singular values. On one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either
Externí odkaz:
http://arxiv.org/abs/2011.08267
Autor:
Aspenberg, Magnus, Cui, Weiwei
Publikováno v:
Trans. Amer. Math. Soc. 374 (2021), no. 9, 6145-6178
We give a complete description of the possible Hausdorff dimensions of escaping sets for meromorphic functions with a finite number of singular values. More precisely, for any given $d\in [0,2]$ we show that there exists such a meromorphic function f
Externí odkaz:
http://arxiv.org/abs/2004.11283
Autor:
Aspenberg, Magnus, Pérez, Rodrigo
It is well known that Gaussian polynomials (i.e., $q$-binomials) describe the distribution of the $area$ statistic on monotone paths in a rectangular grid. We introduce two new statistics, $corners$ and $cindex$; attach ``ornaments'' to the grid; and
Externí odkaz:
http://arxiv.org/abs/2004.01968
Publikováno v:
Discrete and Continuous Dynamical Systems 42 (2022) 679-706
We associate to a perturbation $(f_t)$ of a (stably mixing) piecewise expanding unimodal map $f_0$ a two-variable fractional susceptibility function $\Psi_\phi(\eta, z)$, depending also on a bounded observable $\phi$. For fixed $\eta \in (0,1)$, we s
Externí odkaz:
http://arxiv.org/abs/1910.00369