Düz Disklerdeki Bilardo Akışlarının Topolojik Geçişliliği

Research Article

Year 2020, Volume: 7 Issue: 100. Yıl Özel Sayı, 289 - 298, 23.03.2020

https://doi.org/10.35193/bseufbd.589337

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

[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

[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.

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

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