TIME-DEPENDENT BILLIARDS

被引：43
作者：
KOILLER, J
MARKARIAN, R
KAMPHORST, SO
DECARVALHO, SP
机构：
[1] UNIV REPUBL,FAC INGN,INST MATEMAT & ESTADIST PROF ING RAFAEL LAGUARDIA,BR-21945970 RIO JANEIRO,BRAZIL
[2] UNIV FED MINAS GERAIS,ICEX,DEPT MATEMAT,BR-30161970 BELO HORIZONT,MG,BRAZIL
[3] UNIV FED RIO DE JANEIRO,INST MATEMAT,BR-21945970 RIO JANEIRO,BRAZIL
来源：
NONLINEARITY | 1995年 / 8卷 / 06期
关键词：
D O I：
10.1088/0951-7715/8/6/006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This is an attempt to study mathematically billiards with moving boundaries. We assume that the boundary remains closed, regular and strictly convex, deforming periodically in time, in the normal direction. We describe the associated billiard diffeomorphism and the corresponding invariant measure. We discuss the stability of 2-periodic orbits and investigate the boundedness of the velocity in some precise examples. Finally, we present the Hamiltonian formalism and the symplectic structure, considering that a moving billiard is a billiard with rigid boundary on an augmented configuration space, with a singular metric.
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收藏
页码：983 / 1003
页数：21
相关论文
共 24 条
  • [1] ONE-BODY DISSIPATION AT INTERMEDIATE NUCLEAR CONNECTION REGIMES
    ABAL, G
    DONANGELO, R
    DORSO, CO
    [J]. PHYSICAL REVIEW C, 1992, 46 (01): : 380 - 381
  • [2] [Anonymous], 1978, MATH METHODS CLASSIC, DOI [DOI 10.1007/978-1-4757-1693-1, 10.1007/978-1-4757-1693-1]
  • [3] BERRY MV, 1991, HOUCHES LECTURE SERI, V52, P251
  • [4] Birkhoff G.D, 1927, DYNAM SYST
  • [5] Cornfeld Isaac P., 1982, ERGODIC THEORY, V245
  • [6] Douady R., 1982, THESIS U PARIS 7
  • [7] DOVBYSH SA, 1992, PMM-J APPL MATH MEC+, V56, P188
  • [8] Fermi E., 1949, PHYS REV, V75, P1169, DOI [10.1103/PhysRev.75.1169, DOI 10.1103/PHYSREV.75.1169]
  • [9] ACOUSTICS - TIME-REVERSED SOUND-WAVES RESONATE AMONG PHYSICISTS
    GLANZ, J
    [J]. SCIENCE, 1994, 265 (5171) : 474 - 475
  • [10] KOILLER J, 1994, STATIC TIME DEPENDEN
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