Fixed point of the parabolic renormalization operator

著者

• Lanford, Oscar E.
• Yampolsky, Michael

書誌事項

Fixed point of the parabolic renormalization operator

Oscar E. Lanford III, Michael Yampolsky

（SpringerBriefs in mathematics）

Springer, c2014

注記

Includes bibliographical references

内容説明・目次

内容説明

This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point. Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, Ecalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization. The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics.

目次

1 Introduction.- 2 Local dynamics of a parabolic germ.- 3 Global theory.- 4 Numerical results.- 5 For dessert: several amusing examples.- Index.

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詳細情報

• NII書誌ID(NCID): BB17577772
• ISBN:
  • 9783319117065
• LCCN: 2014951732
• 出版国コード: sz
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cham
• ページ数/冊数: viii, 111 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BB06225285