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In the previous chapters we prepared the stage to prove the essential and most delicate ingredient of renormalization theory, namely consecutive renormalizations of circle diffeomorphisms converge exponentially fast to the set of rotations. Unfortunately the picture is more complicated than what one would wish for; in particular there are examples where one does not see convergence at all. These examples will be discussed in Chap. 9 .

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Exponential Convergence

  • 章节

  • 发表日期：

    2025年

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  • Yiheng Dong,
  • Marco Martens,
  • Liviana Palmisano

摘要

In the previous chapters we prepared the stage to prove the essential and most delicate ingredient of renormalization theory, namely consecutive renormalizations of circle diffeomorphisms converge exponentially fast to the set of rotations. Unfortunately the picture is more complicated than what one would wish for; in particular there are examples where one does not see convergence at all. These examples will be discussed in Chap. 9 .