no. 3
The field of definition for dynamical systems on ℙ 1
Compositio Mathematica, Tome 98 (1995) no. 3, pp. 269-304 
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     zbl = {0849.11090},
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     url = {https://www.numdam.org/item/CM_1995__98_3_269_0/}
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Silverman, Joseph H. The field of definition for dynamical systems on $\mathbb {P}^1$. Compositio Mathematica, Tome 98 (1995) no. 3, pp. 269-304. https://www.numdam.org/item/CM_1995__98_3_269_0/

1 Artin, E. and Tate, J.: Class Field Theory, Benjamin New York, 1967. | Zbl | MR

2 Beardon, A.: Iteration of Rational Functions, Graduate Texts in Math. 132, Springer-Verlag, New York, 1991. | Zbl | MR

3 Ben-Menahem, S.: p-adic iterations, TAUP-1627-88 preprint, March 1, 1988.

4 Call, G. and Silverman, J.H.: Canonical heights on varieties with morphisms, Compositio Math. 89 (1993), 163-205. | Zbl | MR | Numdam

5 Couveignes, J.-M.: Calcul et rationalité de fonctions de Belyi en genre 0, Fourier Annales (to appear). | Zbl | MR | Numdam

6 Denis, L.: Arithmétique et automorphismes affine, preprint, November 1993.

7 Devaney, R.: An Introduction to Chaotic Dynamical Systems, 2nd ed., Addison-Wesley, Redwood City, CA, 1989. | Zbl | MR

8 Hartshorne, R.: Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, New York, 1978. | Zbl | MR

9 Lang, S.: Fundamentals of Diophantine Geometry, Springer-Verlag, New York, 1983. | Zbl | MR

10 Morton, P.: Arithmetic properties of periodic points of quadratic maps, Acat Arith. LXII (1992), 343-372. | Zbl | MR

11 Morton, P. and Silverman, J.H.: Periodic points, multiplicities, and dynamical units, J. Reine ang. Math. (to appear). | Zbl | MR

12 Morton, P. and Silverman, J.H.: Rational periodic points of rational functions, Inter. Math. Research Notices 2 (1994), 97-109. | Zbl | MR

13 Mumford, D. and Fogarty, J.: Geometric Invariant Theory 2nd ed., Springer-Verlag, Berlin, 1982. | Zbl | MR

14 Narkiewicz, W.: Polynomial cycles in algebraic number fields, Colloquium Math. 58 (1989), 151-155. | Zbl | MR

15 Pezda, T.: Polynomial cycles in certain local domains, Acta Arith. LXVI (1994), 11-22. | Zbl | MR

16 Pezda, T.: Cycles of polynomial mappings in several variables, preprint, 1993. | Zbl | MR

17 Russo, P. and Walde, R.: Rational periodic points of the quadratic function Qc(x) = x2 + c, Am. Math. Monthly (1994) (to appear). | Zbl | MR

18 Serre, J.- P.: Local Fields, Springer-Verlag, New York, 1979. | Zbl | MR

19 Serre, J.- P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), 259-331. | Zbl | MR

20 Shimura, G.: 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. | Zbl | MR

21 Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Forms, Iwanami Shoten and Princeton University Press, Princeton, NJ, 1971. | Zbl

22 Silverberg, A.: Fields of definition for homomorphisms of abelian varieties, J. Pure Appl. Algebra 77 (1992), 253-262. | Zbl | MR

23 Silverberg, A. and Zarhin, Yu.: Isogenies of abelian varieties, J. Pure Appl. Algebra 90 (1993), 23-37. | Zbl | MR

24 Silverman, J.H.: The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer-Verlag, Berlin, New York, 1986. | Zbl | MR

25 Silverman, J.H.: Integer points, Diophantine approximation, and iteration of rational maps, Duke Math. J. 71 (1993), 793-829. | Zbl | MR

26 Silverman, J.H.: Geometric and arithmetic properties of the Hénon map, Math. Zeit. 215 (1994), 237-250. | Zbl | MR

27 Thiran, E., Verstegen, D. and Weyers, J.: p-adic dynamics, J. Statistical Physics 54 (1989), 893-913. | Zbl | MR

28 Verstegen, D.: p-adic dynamical systems, in J.-M. Luck, P. Moussa, M. Waldschmidt (eds), Number Theory and Physics, Springer-Verlag, Berlin, 1990, pp. 235-242. | Zbl | MR

29 Weber, H.: Lehrbuch der Algebra, vol. II, Braunschweig, 1899. | JFM