کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1897840 | 1044595 | 2008 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hyperbolic billiards with nearly flat focusing boundaries, I
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
The standard Wojtkowski–Markarian–Donnay–Bunimovich technique for the hyperbolicity of focusing or mixed billiards in the plane requires the diameter of a billiard table to be of the same order as the largest ray of curvature along the focusing boundary. This is due to the physical principle that is used in the proofs, the so-called defocusing mechanism of geometrical optics. In this paper we construct examples of hyperbolic billiards with a focusing boundary component of arbitrarily small curvature whose diameter is bounded by a constant independent of that curvature. Our proof employs a nonstandard cone bundle that does not solely use the familiar dispersing and defocusing mechanisms.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 237, Issue 18, September 2008, Pages 2272–2281
Journal: Physica D: Nonlinear Phenomena - Volume 237, Issue 18, September 2008, Pages 2272–2281
نویسندگان
Luca Bussolari, Marco Lenci,