Bounce trajectories in plane tubular domains

Roberto Peirone

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1989)

  • Volume: 83, Issue: 1, page 39-42
  • ISSN: 0392-7881

Abstract

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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.

How to cite

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Peirone, Roberto. "Bounce trajectories in plane tubular domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 83.1 (1989): 39-42. <http://eudml.org/doc/289029>.

@article{Peirone1989,
abstract = {We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.},
author = {Peirone, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Tubular domains; Bounce trajectories; Illumination of domains},
language = {eng},
month = {12},
number = {1},
pages = {39-42},
publisher = {Accademia Nazionale dei Lincei},
title = {Bounce trajectories in plane tubular domains},
url = {http://eudml.org/doc/289029},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Peirone, Roberto
TI - Bounce trajectories in plane tubular domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 39
EP - 42
AB - We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
LA - eng
KW - Tubular domains; Bounce trajectories; Illumination of domains
UR - http://eudml.org/doc/289029
ER -

References

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  1. ANDERSON, K.G. and MELROSE, R.B., 1977. The propagation of singularities along gliding rays. Invent. Math., 41: 197-232. Zbl0373.35053MR494322DOI10.1007/BF01403048
  2. BUTTAZZO, G. and PERCIVALE, D., 1981. The bounce problem on n-dimensional Riemannian manifolds. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 70: 246-250. 
  3. BUTTAZZO, G. and PERCIVALE, D., 1983. On the approximation of the elastic bounce problem on Riemannian manifolds. J. Differential Equations, 47: 227-245. Zbl0498.58011MR688104DOI10.1016/0022-0396(83)90035-9
  4. CARRIERO, M. and PASCALI, E., 1980. Il problema del rimbalzo unidimensionale e sue approssimazioni con penalizzazioni non convesse. Rend. Mat., 13: 541-553. Zbl0461.73049
  5. DEGIOVANNI, M., 1984. Multiplicity of solutions for the bounce problem. J. Differential Equations, 54: 414-428. Zbl0505.34006MR760380DOI10.1016/0022-0396(84)90152-9
  6. GUY, R. and KLEE, V., 1971. Monthly research problems 1969-71. Amer. Math. Month., 78: 1113-1122. MR1536553DOI10.2307/2316321
  7. MELROSE, R.B. and SJÖSTRAND, J., 1982. Singularities of boundary value problems. II. Comm. Pure App. Math., 35: 129-168. Zbl0546.35083MR644020DOI10.1002/cpa.3160350202
  8. PENROSE, L. and PENROSE, R., 1958. Puzzles for Christmas. The New Scientist, 25 Dec. 1958: 1580-81 and 1597. 
  9. PETKOV, V.M., 1984-85. Propriétés génériques des rayons réfléchissants et applications aux problèmes spectraux. Séminaire Bony-Sjöstrand-Meyer. 
  10. RAUCH, J., 1978. Illumination of bounded domains. Amer. Math. Month., 85: 359-361. Zbl0399.52006MR482537DOI10.2307/2321342
  11. SINAI, JA.G., 1970. Dynamicl systems with elastic reflections. Ergodic properties of dispersing billiards (Russian). Uspehi Mat. Nauk, 25 (2): 141-192. MR274721
  12. SINAI, JA.G., 1978. Billiard trajectories in a polyhedral angle (Russian). Uspehi Mat. Nauk, 33 (1): 229-230. Zbl0415.28021MR488170

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