# Construction of K-stable foliations for two-dimensional dispersing billiards without eclipse

## 抄録

Let T be the billiard map for a two-dimensional dispersing billiard without eclipse. We show that the nonwandering set Ω<SUP>+</SUP> for T has a hyperbolic structure quite similar to that of the horseshoe. We construct a sort of stable foliation for (Ω<SUP>+</SUP>, T) each leaf of which is a K-decreasing curve. We call the foliation a K-stable foliation for (Ω<SUP>+</SUP>, T). Moreover, we prove that the foliation is Lipschitz continuous with respect to the Euclidean distance in the so called (r, \varphi)-coordinates. It is well-known that we can not always expect the existence of such a Lipschitz continuous invariant foliation for a dynamical system even if the dynamical system itself is smooth. Therefore, we keep our construction as elementary and self-contained as possible so that one can see the concrete structure of the set Ω<SUP>+</SUP> and why the K-stable foliation turns out to be Lipschitz continuous.

## 収録刊行物

• Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 56(3), 803-831, 2004-07-01

The Mathematical Society of Japan

## 各種コード

• NII論文ID(NAID)
10013358966
• NII書誌ID(NCID)
AA0070177X
• 本文言語コード
ENG
• 資料種別
ART
• ISSN
00255645
• NDL 記事登録ID
7015172
• NDL 雑誌分類
ZM31(科学技術--数学)
• NDL 請求記号
Z53-A209
• データ提供元
CJP書誌  NDL  J-STAGE

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