ON THE ELLIPTIC TIME IN THE ADELIC GRAVITY
Abstract
The paper is devoted to the algebraic and arithmetic structures related to the two- body problem and discuss the possible generalizations. The role of the points of finite order on the elliptic curves is emphasized.
Keywords
Full Text:
PDFReferences
M. Atiyah, R. Dijkgraaf, N. Hitchin: Geometry and physics. Phil. Trans. R. Soc. A 368 (2010) 913–926.
M. Atiyah, V. Drinfeld, N. Hitchin, Y. Manin: Construction of instantons. Physics Letters A 65 (3) (1978), 185–187.
A. Buium, Y. I. Manin: Arithmetic Differential Equations of Painleve VI Type. arXiv:1307.3841v2 [math.NT].
D. A. Cox, S. Katz: Mirror Symmetry and Algebraic Geometry. American Mathematical Soc., 1999.
V. Dremov, G. Shabat and P. Vytnova: On dynamical systems with 2-adic time. Proceedings of The Steklov Institute of Mathematics 265 (2009) 101–109.
M. Kontsevich: Intersection Theory on the Moduli Space of Curves and the Matrix Airy FunctionCommun. Math. Phys. 147 (1992) 1-23.
M. Kontsevich, A. Schwarz, V. Vologodsky: Integrality of instanton numbers and p-adic B-model. arXiv:hep-th/0603106.
N. J. Hitchin: Twistor spaces, Einstein metrics and isomonodromic deformations. J. Differential Geom. 42 (1995), no. 1, 30–112.
N. J. Hitchin: Poncelet polygons and the Painlev´e equations. Geometry and analysis (Bombay, 1992), Tata Inst. Fund. Res., Bombay, 1995.
S. K. Lando and A. K. Zvonkin: Graphs on Surfaces and Their Applications (with Appendix by Don B. Zagier). Springer-Verlag, 2004.
Y. Manin: Reflections on arithmetical physics. In Conformal invariance and string theory, pp. 293–303, Academic Press, Boston, MA, 1989.
G. Moore: Arithmetic and Attractors. arXiv:hep-th/9807087.
G. Shabat: p-adic entropies of logistic maps. Proc. Steklov Math. Inst. 245 (2004) 257-263.
K. P. Tod: Self-dual Einstein metrics from the Painleve VI equation. Phys. Lett, A190 221-224.
V. A. Voevodsky and G. B. Shabat: Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields. Dokl. Akad. Nauk SSSR 304 (1989) 265–268.
E. Witten: Two dimensional gravity and intersection theory on moduli space. Surveys in Diff. Geom. 1 (1991) 243–310.
Refbacks
- There are currently no refbacks.
ISSN 0354-4656 (print)
ISSN 2406-0879 (online)