@article{CM_1995__98_3_269_0, author = {Silverman, Joseph H.}, title = {The field of definition for dynamical systems on $\mathbb {P}^1$}, journal = {Compositio Mathematica}, pages = {269--304}, publisher = {Kluwer Academic Publishers}, volume = {98}, number = {3}, year = {1995}, mrnumber = {1351830}, zbl = {0849.11090}, language = {en}, url = {http://www.numdam.org/item/CM_1995__98_3_269_0/} }
Silverman, Joseph H. The field of definition for dynamical systems on $\mathbb {P}^1$. Compositio Mathematica, Tome 98 (1995) no. 3, pp. 269-304. http://www.numdam.org/item/CM_1995__98_3_269_0/
1 Class Field Theory, Benjamin New York, 1967. | MR | Zbl
and :2 Iteration of Rational Functions, Graduate Texts in Math. 132, Springer-Verlag, New York, 1991. | MR | Zbl
:3 p-adic iterations, TAUP-1627-88 preprint, March 1, 1988.
:4 Canonical heights on varieties with morphisms, Compositio Math. 89 (1993), 163-205. | Numdam | MR | Zbl
and :5 Calcul et rationalité de fonctions de Belyi en genre 0, Fourier Annales (to appear). | Numdam | MR | Zbl
:6 Arithmétique et automorphismes affine, preprint, November 1993.
:7 An Introduction to Chaotic Dynamical Systems, 2nd ed., Addison-Wesley, Redwood City, CA, 1989. | MR | Zbl
:8 Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, New York, 1978. | MR | Zbl
:9 Fundamentals of Diophantine Geometry, Springer-Verlag, New York, 1983. | MR | Zbl
:10 Arithmetic properties of periodic points of quadratic maps, Acat Arith. LXII (1992), 343-372. | MR | Zbl
:11 Periodic points, multiplicities, and dynamical units, J. Reine ang. Math. (to appear). | MR | Zbl
and :12 Rational periodic points of rational functions, Inter. Math. Research Notices 2 (1994), 97-109. | MR | Zbl
and :13 Geometric Invariant Theory 2nd ed., Springer-Verlag, Berlin, 1982. | MR | Zbl
and :14 Polynomial cycles in algebraic number fields, Colloquium Math. 58 (1989), 151-155. | MR | Zbl
:15 Polynomial cycles in certain local domains, Acta Arith. LXVI (1994), 11-22. | MR | Zbl
:16 Cycles of polynomial mappings in several variables, preprint, 1993. | MR | Zbl
:17 Rational periodic points of the quadratic function Qc(x) = x2 + c, Am. Math. Monthly (1994) (to appear). | MR | Zbl
and :18 P.: Local Fields, Springer-Verlag, New York, 1979. | MR | Zbl
-19 P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), 259-331. | MR | Zbl
-20 On the field of definition for a field of automorphic functions.I, Annals of Math. 80 (1964), 160-189; II, 81 (1965), 124-165; III, 83 (1965), 377-385. | MR | Zbl
:21 Introduction to the Arithmetic Theory of Automorphic Forms, Iwanami Shoten and Princeton University Press, Princeton, NJ, 1971. | Zbl
:22 Fields of definition for homomorphisms of abelian varieties, J. Pure Appl. Algebra 77 (1992), 253-262. | MR | Zbl
:23 Isogenies of abelian varieties, J. Pure Appl. Algebra 90 (1993), 23-37. | MR | Zbl
and :24 The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer-Verlag, Berlin, New York, 1986. | MR | Zbl
:25 Integer points, Diophantine approximation, and iteration of rational maps, Duke Math. J. 71 (1993), 793-829. | MR | Zbl
:26 Geometric and arithmetic properties of the Hénon map, Math. Zeit. 215 (1994), 237-250. | MR | Zbl
:27 p-adic dynamics, J. Statistical Physics 54 (1989), 893-913. | MR | Zbl
, and :28 p-adic dynamical systems, in J.-M. Luck, P. Moussa, M. Waldschmidt (eds), Number Theory and Physics, Springer-Verlag, Berlin, 1990, pp. 235-242. | MR | Zbl
:29 Lehrbuch der Algebra, vol. II, Braunschweig, 1899. | JFM
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