Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Geyer, Lukas"'
One of the fundamental distinctions in McMullen and Sullivan's description of the Teichm\"uller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental enti
Externí odkaz:
http://arxiv.org/abs/2405.15667
Autor:
Geyer, Lukas, Hlushchanka, Mikhail
We provide a complete combinatorial classification of critically fixed anti-Thurston maps, i.e., orientation-reversing branched covers of the 2-sphere that fix every critical point. The first step in the proof, and an interesting result in its own ri
Externí odkaz:
http://arxiv.org/abs/2006.10788
Autor:
Geyer, Lukas
We prove that unicritical polynomials $f(z)=z^d+c$ which are semihyperbolic, i.e., for which the critical point $0$ is a non-recurrent point in the Julia set, are uniformly expanding on the Julia set with respect to the metric $\rho(z) |dz|$, where $
Externí odkaz:
http://arxiv.org/abs/1910.12898
Autor:
Geyer, Lukas, Wildrick, Kevin
Publikováno v:
Proc. Amer. Math. Soc. 146 (2018), no. 1, 281-293
Bonk and Kleiner showed that any metric sphere which is Ahlfors 2-regular and linearly locally contractible is quasisymmetrically equivalent to the standard sphere, in a quantitative way. We extend this result to arbitrary metric compact orientable s
Externí odkaz:
http://arxiv.org/abs/1610.08896
Autor:
Geyer, Lukas
Publikováno v:
Indiana Univ. Math. J. 68 (2019), no. 5, 1551-1578
Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this is sharp
Externí odkaz:
http://arxiv.org/abs/1507.02666
Autor:
Geyer, Lukas
Publikováno v:
Illinois J. Math. 58 (2014), no. 1, 279-284
In 1952, Littlewood stated a conjecture about the average growth of spherical derivatives of polynomials, and showed that it would imply that for entire function of finite order, "most" preimages of almost all points are concentrated in a small subse
Externí odkaz:
http://arxiv.org/abs/1404.0983
Autor:
Geyer, Lukas
Publikováno v:
Indiana University Mathematics Journal, 2019 Jan 01. 68(5), 1551-1578.
Externí odkaz:
https://www.jstor.org/stable/26958336
Autor:
GEYER, LUKAS, WILDRICK, KEVIN
Publikováno v:
Proceedings of the American Mathematical Society, 2018 Jan 01. 146(1), 281-293.
Externí odkaz:
https://www.jstor.org/stable/90016426
Autor:
Geyer, Lukas
Publikováno v:
Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 2, 439-442
X. Buff and A. Cheritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of A. Avila, we give yet another simplification of their proof. The main tool used is a harmonic function introd
Externí odkaz:
http://arxiv.org/abs/math/0510578
Autor:
Geyer, Lukas
Publikováno v:
Proc. Amer. Math. Soc. 136 (2008), no. 2, 549-555
D. Khavinson and G. Swiatek proved that harmonic polynomials p(z)+q(z), where p is holomorphic, q is antiholomorphic, and deg p = n > 1 = deg q, can have at most 3n-2 complex zeros. We show that this bound is sharp for all n by proving a conjecture o
Externí odkaz:
http://arxiv.org/abs/math/0510539