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Renormalization and Siegel disks for complex Hénon maps
Journal of the European Mathematical Society ( IF 2.6 ) Pub Date : 2020-12-07 , DOI: 10.4171/jems/1028 Denis Gaidashev 1 , Remus Radu 2 , Michael Yampolsky 3
Journal of the European Mathematical Society ( IF 2.6 ) Pub Date : 2020-12-07 , DOI: 10.4171/jems/1028 Denis Gaidashev 1 , Remus Radu 2 , Michael Yampolsky 3
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We use hyperbolicity of golden-mean renormalization of dissipative H\'enon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex H\'enon maps with golden-mean rotation number are topological circles. Conditionally on an appropriate renormalization hyperbolicity property, we derive the same result for Siegel disks of H\'enon maps with all eventually periodic rotation numbers.
中文翻译:
复杂 Hénon 映射的重整化和 Siegel 盘
我们利用耗散类H\'enon映射的黄金平均重整化的双曲线证明了具有黄金平均旋转数的足够耗散二次复H\'enon映射的Siegel圆盘的边界是拓扑圆。以适当的重整化双曲性质为条件,我们对 H\'enon 映射的 Siegel 圆盘得出相同的结果,这些盘具有所有最终周期旋转数。
更新日期:2020-12-07
中文翻译:
复杂 Hénon 映射的重整化和 Siegel 盘
我们利用耗散类H\'enon映射的黄金平均重整化的双曲线证明了具有黄金平均旋转数的足够耗散二次复H\'enon映射的Siegel圆盘的边界是拓扑圆。以适当的重整化双曲性质为条件,我们对 H\'enon 映射的 Siegel 圆盘得出相同的结果,这些盘具有所有最终周期旋转数。