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Renormalization in the Golden-Mean Semi-Siegel Henon Family: Universality and Non-Rigidity

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 نشر من قبل Jonguk Yang JY
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Jonguk Yang




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It was recently shown by Gaidashev and Yampolsky that appropriately defined renormalizations of a sufficiently dissipative golden-mean semi-Siegel Henon map converge super-exponentially fast to a one-dimensional renormalization fixed point. In this paper, we show that the asymptotic two-dimensional form of these renormalizations is universal, and is parameterized by the average Jacobian. This is similar to the limit behavior of period-doubling renormalization in the Henon family considered by de Carvalho, Lyubich and Martens. As an application of our result, we prove that the boundary of the golden-mean Siegel disk of a dissipative Henon map is non-rigid.



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