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Düz Disklerdeki Bilardo Akışlarının Topolojik Geçişliliği

Year 2020, Volume: 7 Issue: 100. Yıl Özel Sayı, 289 - 298, 23.03.2020
https://doi.org/10.35193/bseufbd.589337

Abstract

Sabit bir iç açı datasına sahip her
düz diskler ailesinin bilardo akışı topolojik geçişli olan yoğun bir Gδ
kümesi içerdiğini gösteriyoruz.

References

  • [1] Gutkin, E. (1996). Billiards in polygons: survey of recent results. Journal of statistical physics, 83(1), 7-26.
  • [2] Gutkin, E. (2003). Billiard dynamics: a survey with the emphasis on open problems. Regular and chaotic dynamics, 8(1), 1-13.
  • [3] Masur, H. (2006). Ergodic theory of translation surfaces. Handbook of dynamical systems 1B. Elsevier, 527-547.
  • [4] Zorich, A. (2006). Frontiers in number theory, physics, and geometry I, APA, 439-585
  • [5] Masur, H. & Tabachnikov, S. (2002). Rational billiards and flat structures. Handbook of dynamical systems 1A. Elsevier, 1015-1089.
  • [6] Sağlam, İ. (2016). Flat Surfaces with Finite Holonomy Group. arXiv preprint arXiv:1612.07169.
  • [7] Zemlyakov, A. N., & Katok, A. B. (1975). Topological transitivity of billiards in polygons. Mathematical Notes of the Academy of Sciences of the USSR, 18(2), 760-764.
  • [8] Troyanov, M. (2007). On the Moduli Space of Singular Euclidean Surfaces. Handbook of Teichmüller Theory 1, AMS, 507–540.
  • [9] Troyanov, M. (1986). Les surfaces euclidienne à singularités coniques. L’Enseignement Math. EMS, 79–94.
  • [10] Troyanov, M. (1991). Prescribing curvature on compact surfaces with conical singularities. Transactions of the American Mathematical Society, 324(2), 793-821.
  • [11] Hulin, D.,& Troyanov, M. (1992). Prescribing curvature on open surfaces. Mathematische Annalen, 293(1), 277-315.
  • [12] Sağlam, İ. (2016). Complete Flat Cone Metrics on Surfaces. arXiv preprint arXiv:1602.04240.
Year 2020, Volume: 7 Issue: 100. Yıl Özel Sayı, 289 - 298, 23.03.2020
https://doi.org/10.35193/bseufbd.589337

Abstract

References

  • [1] Gutkin, E. (1996). Billiards in polygons: survey of recent results. Journal of statistical physics, 83(1), 7-26.
  • [2] Gutkin, E. (2003). Billiard dynamics: a survey with the emphasis on open problems. Regular and chaotic dynamics, 8(1), 1-13.
  • [3] Masur, H. (2006). Ergodic theory of translation surfaces. Handbook of dynamical systems 1B. Elsevier, 527-547.
  • [4] Zorich, A. (2006). Frontiers in number theory, physics, and geometry I, APA, 439-585
  • [5] Masur, H. & Tabachnikov, S. (2002). Rational billiards and flat structures. Handbook of dynamical systems 1A. Elsevier, 1015-1089.
  • [6] Sağlam, İ. (2016). Flat Surfaces with Finite Holonomy Group. arXiv preprint arXiv:1612.07169.
  • [7] Zemlyakov, A. N., & Katok, A. B. (1975). Topological transitivity of billiards in polygons. Mathematical Notes of the Academy of Sciences of the USSR, 18(2), 760-764.
  • [8] Troyanov, M. (2007). On the Moduli Space of Singular Euclidean Surfaces. Handbook of Teichmüller Theory 1, AMS, 507–540.
  • [9] Troyanov, M. (1986). Les surfaces euclidienne à singularités coniques. L’Enseignement Math. EMS, 79–94.
  • [10] Troyanov, M. (1991). Prescribing curvature on compact surfaces with conical singularities. Transactions of the American Mathematical Society, 324(2), 793-821.
  • [11] Hulin, D.,& Troyanov, M. (1992). Prescribing curvature on open surfaces. Mathematische Annalen, 293(1), 277-315.
  • [12] Sağlam, İ. (2016). Complete Flat Cone Metrics on Surfaces. arXiv preprint arXiv:1602.04240.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İsmail Sağlam 0000-0002-1283-6396

Ahmet Refah Torun 0000-0001-7213-5228

Publication Date March 23, 2020
Submission Date July 9, 2019
Acceptance Date March 3, 2020
Published in Issue Year 2020 Volume: 7 Issue: 100. Yıl Özel Sayı

Cite

APA Sağlam, İ., & Torun, A. R. (2020). Düz Disklerdeki Bilardo Akışlarının Topolojik Geçişliliği. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 7(100. Yıl Özel Sayı), 289-298. https://doi.org/10.35193/bseufbd.589337