EXAMPLES OF PROJECTIVE BILLIARDS WITH OPEN SETS OF PERIODIC ORBITS

被引：0
作者：
Fierobe, Corentin [1 ]
机构：
[1] IST Austria, Klosterneuburg, Austria
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2024年 / 44卷 / 11期
关键词：
Billiards; systems with impacts; projective billiards; periodic orbits; open sets of periodic orbits; periodic points; Ivrii's conjecture; Weyl's law; POINTS;
D O I：
10.3934/dcds.2024059
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the class of projective billiards, which contains the usual billiards, we exhibit counter -examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter -examples are polygons admitting a 2 -parameters family of n -periodic orbits, with n being either 3 or any even integer greater than 4.
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收藏
页码：3287 / 3301
页数：15
相关论文
共 14 条
  • [1] Baryshnikov Yu., 2005, J. Math. Sci, V128, P2706
  • [2] Three-Period Orbits in Billiards on the Surfaces of Constant Curvature
    Blumen, Victoria
    Kim, Ki Yeun
    Nance, Joe
    Zharnitsky, Vadim
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012, 2012 (21) : 5014 - 5024
  • [3] On Quadrilateral Orbits in Planar Billiards
    Glutsyuk, A. A.
    Kudryashov, Yu G.
    [J]. DOKLADY MATHEMATICS, 2011, 83 (03) : 371 - 373
  • [4] On 4-Reflective Complex Analytic Planar Billiards
    Glutsyuk, Alexey
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2017, 27 (01) : 183 - 238
  • [5] NO PLANAR BILLIARD POSSESSES AN OPEN SET OF QUADRILATERAL TRAJECTORIES
    Glutsyuk, Alexey
    Kudryashov, Yury
    [J]. JOURNAL OF MODERN DYNAMICS, 2012, 6 (03) : 287 - 326
  • [6] RYCHLIK MR, 1989, J DIFFER GEOM, V30, P191
  • [7] STOJANOV L, 1991, J DIFFER GEOM, V34, P835
  • [8] ON THE DUAL BILLIARD PROBLEM
    TABACHNIKOV, S
    [J]. ADVANCES IN MATHEMATICS, 1995, 115 (02) : 221 - 249
  • [9] Introducing projective billiards
    Tabachnikov, S
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1997, 17 : 957 - 976
  • [10] TABACHNIKOV S., 1995, PANOR SYNTH
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