具有正面积边界的相对紧siegel盘-凯发娱乐官网

具有正面积边界的相对紧siegel盘
relatively compact siegel diskswith boundaries of positive area
doi: , ,   
作者: 孙丹隽, 曲宏宇:北京邮电大学理学院,北京
关键词: ;;;;;
摘要: perez-marco用管状黎曼曲面构造了具有c边界的相对紧siegel盘。cheritat改进了此技术, 并且构造了具有伪圆边界的相对紧siegel盘。本文基于此技术构造了具有正面积边界相对 紧siegel盘的全纯映射。给出的例子定义域为复平面的子集。
abstract: perez-marco used tube-log riemann surfaces to construct relatively compact siegel disks with c boundaries. cheritat developed the technique and constructed rela- tively compact siegel disks with pseudo-cirle boundaries. in this paper, based on the technique, we construct holomorphic maps with relatively compact siegel disks whose boundaries have positive area. the examples are defined on a subset of ℂ.
文章引用:孙丹隽, 曲宏宇. 具有正面积边界的相对紧siegel盘[j]. 理论数学, 2024, 14(2): 799-806.

参考文献

[1] brjuno, a.d. (1965) on convergence of transforms of differential equations to the normal form. doklady akademii nauk sssr, 165, 987-989.
[2] brjuno, a.d., eskin, g.i., genov, g.k., et al. (1971) transactions of the moscow mathematical society. vol. 25, american mathematical society, providence, 131-288.
[3] cheraghi, d. (2019) typical orbits of quadratic polynomials with a neutral fixed point: non-brjuno type. annales scientifiques de l'ens, 52, 59-138.
[4] siegel, c.l. (1942) iteration of analytic functions. annals of mathematics, 43, 607-612.
[5] yang, f. (2023) siegel disks and related topics.
[6] cremer, h. (1928) zum zentrumproblem. mathematische annalen, 98, 151-163.
[7] geyer, l. (2019) linearizability of saturated polynomials. indiana university mathematics journal, 68, 1551-1578.
[8] yoccoz, j.-c. (1988) linearisation des germes de diffeomorphismes holomorphes de (c, 0). comptes rendus de l'academie des sciences, 306, 55-58.
[9] perez-marco, r. (1997) siegel disks with smooth boundaries. preprint.
[10] avila, a., buff, x. and cheritat, a. (2004) siegel disks with smooth boundaries. acta math- ematica, 193, 1-30.
[11] buff, x. and cheritat, a. (2007) how regular can the boundary of a quadratic siegel disk be? proceedings of the american mathematical society, 135, 1073-1080.
[12] cheritat, a. (2011) relatively compact siegel disks with non-locally connected boundaries. mathematische annalen, 349, 529-542.
[13] biswas, k. (2016) positive area and inaccessible fixed points for hedgehogs. ergodic theory and dynamical systems, 36, 1839-1850.
[14] fu, y. and yang, f. (2020) area and hausdorff dimension of sierpinski carpet julia sets. mathematische zeitschrift, 294, 1441-1456.
[15] cheraghi, d., dezotti, a. and yang, f. (2020) dimension paradox of irrationally indifferent attractors. submitted.
为你推荐
凯发娱乐官网的友情链接
网站地图