数論力学
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2021/01/31 06:50 UTC 版)
数論力学（すうろんりきがく、英: Arithmetic dynamics[1]）は、数学における力学系と数論という二つの領域を融合した分野である。
- ^ J.H. Silverman (2007). The Arithmetic of Dynamical Systems. Springer. ISBN 978-0-387-69903-5
- ^ D. G. Northcott. Periodic points on an algebraic variety. Ann. of Math. (2), 51:167--177, 1950.
- ^ P. Morton and J. H. Silverman. Rational periodic points of rational functions. Internat. Math. Res. Notices, (2):97--110, 1994.
- ^ P. Morton. Arithmetic properties of periodic points of quadratic maps. Acta Arith., 62(4):343--372, 1992.
- ^ E. V. Flynn, B. Poonen, and E. F. Schaefer. Cycles of quadratic polynomials and rational points on a genus-2 curve. Duke Math. J., 90(3):435--463, 1997.
- ^ M. Stoll, Rational 6-cycles under iteration of quadratic polynomials, 2008.
- ^ B. Poonen. The classification of rational preperiodic points of quadratic polynomials over Q: a refined conjecture. Math. Z., 228(1):11--29, 1998.
- ^ J. H. Silverman. Integer points, Diophantine approximation, and iteration of rational maps. Duke Math. J., 71(3):793-829, 1993.
- ^ 基本定理は、F(x) ∈ がC(x) であり、ある F の繰り返しが多項式であれば、第二番目の繰り返しは多項式であるという定理
- ^ S.-W. Zhang, Distributions in algebraic dynamics, Differential Geometry: A Tribute to Professor S.-S. Chern, Surv. Differ. Geom., Vol. X, Int. Press, Boston, MA, 2006, pages 381–430.
- ^ R. Rumely and M. Baker, Analysis and dynamics on the Berkovich projective line, ArXiv preprint, 150 pages.
- ^ Equidistribution in number theory, an introduction, Andrew Granville, Zeév Rudnick Springer, 2007, ISBN 978-1-4020-5403-7
- ^ Sidorov, Nikita (2003). “Arithmetic dynamics”. In Bezuglyi, Sergey; Kolyada, Sergiy. Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser.. 310. Cambridge: Cambridge University Press. pp. 145–189. ISBN 0-521-53365-1. Zbl 1051.37007
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