Zobrazeno 1 - 10
of 230
pro vyhledávání: '"Petersen, Carsten"'
Let $K\subset\mathbb{C}$ be non-polar, compact and polynomially convex. We study the limits of equilibrium measures on preimages of compact sets, under $K$-regular sequences of polynomials, that center on $K$ and under the sequences of derivatives of
Externí odkaz:
http://arxiv.org/abs/2312.14740
Let $\Omega \in \mathbb{C}$ be a domain such that $K:= \mathbb{C} \setminus \Omega$ is compact and non-polar. Let $g_\Omega$ be the Green's function with a logarithmic pole at infinity, and let $\omega = \omega_K$ be the equilibrium distribution on $
Externí odkaz:
http://arxiv.org/abs/2312.14655
Suppose $C \subset \mathbb{C}$ is compact. Let $q_k$ be a sequence of polynomials of degree $n_k \to \infty$, such that the locus of roots of all the polynomials is bounded, and the number of roots of $q_k$ in any closed set $L$ not meeting $C$ is un
Externí odkaz:
http://arxiv.org/abs/2312.14519
Autor:
Petersen, Carsten Lunde, Zakeri, Saeed
We study Hausdorff limits of the external rays of a given periodic angle along a convergent sequence of polynomials of degree $d \geq 2$ with connected Julia sets.
Comment: mildly expanded, new appendix and updated references
Comment: mildly expanded, new appendix and updated references
Externí odkaz:
http://arxiv.org/abs/2309.01027
This paper develops a conformal renormalization scheme for compact sets $K \subset \mathbb{C}$. As one application of the conformal renormalization scheme we prove that for every isolated non-trivial connected component $E \subset K$ there exists a c
Externí odkaz:
http://arxiv.org/abs/2111.01924
Autor:
Vuaille, Jeanne, Abrahamsen, Per, Jensen, Signe M., Diamantopoulos, Efstathios, Wacker, Tomke S., Petersen, Carsten T.
Publikováno v:
In Science of the Total Environment 15 June 2024 929
We solve the longstanding conjecture by Milnor (1993) concerning the connectedness locus $M_1$ of the family of quadratic rational maps tangent to the identity at $\infty$. We prove that this locus in homeomorphic to the Mandelbrot set $M$ and that t
Externí odkaz:
http://arxiv.org/abs/2107.09407
Autor:
Christiansen, Jacob Stordal, Henriksen, Christian, Pedersen, Henrik Laurberg, Petersen, Carsten Lunde
We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K in C and compare such limits to K. Moreover, we prove that the measures of maxim
Externí odkaz:
http://arxiv.org/abs/2106.06392
Autor:
Petersen, Carsten L., Zakeri, Saeed
Publikováno v:
Conform. Geom. Dyn. 25 (2021) 170-178
Let $P: {\mathbb C} \to {\mathbb C}$ be a polynomial map with disconnected filled Julia set $K_P$ and let $z_0$ be a repelling or parabolic periodic point of $P$. We show that if the connected component of $K_P$ containing $z_0$ is non-degenerate, th
Externí odkaz:
http://arxiv.org/abs/2009.02788
Autor:
Deniz, Aslı, Petersen, Carsten Lunde
This paper concerns the problem of extending the parameter domain of holomorphic motions to include isolated boundary points, punctures of the domains. Supposing that the parameter domain has an isolated boundary point $\lambda^*$, we explore the ext
Externí odkaz:
http://arxiv.org/abs/2001.03940