On the Circumcenters of Triangular Orbits in Elliptic Billiard

被引：7
|
作者：
Fierobe, Corentin [1 ]
机构：
[1] Ecole Normale Super Lyon, UMR CNRS 5669, Unite Math Pures & Appl, 46 Allee Italie, F-69364 Lyon 07, France
来源：
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2021年 / 27卷 / 04期
关键词：
Billiard; Elliptic billiard; Periodic orbits; Triangular orbits; Complex reflection law; Circumcenters; Ellipse; Conic;
D O I：
10.1007/s10883-021-09537-2
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
On an elliptic billiard, we study the set of the circumcenters of all triangular orbits and we show that this is an ellipse. This article follows Romaskevich (L'Enseig Math 60:247-255, 2014), which proves the same result with the incenters, and Glutsyuk (Moscow Math J 14:239-289, 2014), which among others, introduces the theory of complex reflection in the complex projective plane. The result we present was found at the same time in Garcia (Amer Math Monthly 126:491-504, 2019). His proof uses completely different methods of real differential calculus.
引用
收藏
页码：693 / 705
页数：13
相关论文
共 50 条
  • [1] On the Circumcenters of Triangular Orbits in Elliptic Billiard
    Corentin Fierobe
    Journal of Dynamical and Control Systems, 2021, 27 : 693 - 705
  • [2] On the incenters of triangular orbits on elliptic billiards
    Romaskevich, Olga
    ENSEIGNEMENT MATHEMATIQUE, 2014, 60 (3-4): : 247 - 255
  • [3] New Properties of Triangular Orbits in Elliptic Billiards
    Garcia, Ronaldo
    Reznik, Dan
    Koiller, Jair
    AMERICAN MATHEMATICAL MONTHLY, 2021, : 898 - 910
  • [4] Shedding light on periodic orbits in triangular organic micro-billiard lasers
    Lafargue, C.
    Bittner, S.
    Ulysse, C.
    Grigis, A.
    Zyss, J.
    Lebental, M.
    2013 CONFERENCE ON LASERS AND ELECTRO-OPTICS EUROPE AND INTERNATIONAL QUANTUM ELECTRONICS CONFERENCE (CLEO EUROPE/IQEC), 2013,
  • [5] Polygons in billiard orbits
    Don, Henk
    JOURNAL OF NUMBER THEORY, 2012, 132 (06) : 1151 - 1163
  • [6] Elliptic quantum billiard
    Waalkens, H
    Wiersig, J
    Dullin, HR
    ANNALS OF PHYSICS, 1997, 260 (01) : 50 - 90
  • [7] λ-stability of periodic billiard orbits
    Gaivao, Jose Pedro
    Troubetzkoy, Serge
    NONLINEARITY, 2018, 31 (09) : 4326 - 4353
  • [8] Periodic orbits in outer billiard
    Tumanov, Alexander
    Zharnitsky, Vadim
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2006, 2006
  • [9] Entanglement Entropy in a Triangular Billiard
    Joseph, Sijo K.
    Sanjuan, Miguel A. F.
    ENTROPY, 2016, 18 (03):
  • [10] Triangular billiard in a constant field
    Maslovsky, Yu. N.
    Slipushenko, S. V.
    Tur, A. V.
    Yanovsky, V. V.
    FUNCTIONAL MATERIALS, 2015, 22 (02): : 233 - 244
12345