Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is ...Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.展开更多
We prove that for any bounded type irrational number 0 〈 0 〈 1, the boundary of theSiegel disk of fα（z） = e^2πiθsin（z） ＋ αsin^3（z）, a E C, which centered at the origin, is a quasicircle passing through 2,...We prove that for any bounded type irrational number 0 〈 0 〈 1, the boundary of theSiegel disk of fα（z） = e^2πiθsin（z） ＋ αsin^3（z）, a E C, which centered at the origin, is a quasicircle passing through 2, 4 or 6 critical points of fα counted with multiplicity.展开更多
文摘Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.
基金supported by NSFC(Nos.11601422,11871394)NSF of Education Department of Shaanxi Provincial Government(No.18JK0770)Natural Science Basic Research Plan in Shaanxi Province of China(No.2019JM-419)
基金Supported by National Natural Science Foundation of China(Grant No.11231009)
文摘We prove that for any bounded type irrational number 0 〈 0 〈 1, the boundary of theSiegel disk of fα（z） = e^2πiθsin（z） ＋ αsin^3（z）, a E C, which centered at the origin, is a quasicircle passing through 2, 4 or 6 critical points of fα counted with multiplicity.
