A Self-Affine Property of Evolutional Type Appearing in a Hamilton-Jacobi Flow Starting from the Takagi Function

Yasuhiro Fujita, Nao Hamamuki, Norikazu Yamaguchi

研究成果: ジャーナルへの寄稿学術論文査読

1 被引用数 (Scopus)

抄録

In this paper, we study a Hamilton-Jacobi flow {Ht γ } t>0 starting from the Takagi function γ . The Takagi function is well known as a pathological function that is everywhere continuous and nowhere differentiable on R. As the first result of this paper, we derive an explicit representation of {Ht γ }. It turns out that Ht γ is a piecewise quadratic function at any time and that the points of intersection between the parabolas are given in terms of binary expansion of real numbers. Applying the representation formula, we next give the main result, which asserts that {Ht γ } has a self-affine property of evolutional type involving a time difference in the functional equality. Furthermore, we determine the optimal time until when the self-affine property is valid.

本文言語英語
ページ(範囲)105-120
ページ数16
ジャーナルMichigan Mathematical Journal
71
1
DOI
出版ステータス出版済み - 2022/03

ASJC Scopus 主題領域

  • 数学一般

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