Arithmetic properties of periodic points of quadratic maps, II

• Autorzy: Patrick Morton
• Języki publikacji: EN

Kategorie tematyczne

• 11D41: Higher degree equations; Fermat's equation
• 11F03: Modular and automorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998-1999
• Tom: 87
• Numer: 2
• Strony: 89-102

Daty

wydano

1998

otrzymano

1997-04-23

poprawiono

1998-02-18

Twórcy

autor

Patrick Morton

• Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02481-8203, U.S.A.

Bibliografia

• [ba] E. Bach, Toward a theory of Pollard's rho method, Inform. and Comput. 90 (1991), 139-155.
• [bo] T. Bousch, Sur quelques problèmes de dynamique holomorphe, thèse, Université de Paris-Sud, Centre d'Orsay, 1992.
• [de] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1987.
• [fps] V. Flynn, B. Poonen and E. Schaefer, Cycles of quadratic polynomials and rational points on a genus 2 curve, Duke Math. J. 90 (1997), 435-463.
• [m1] P. Morton, Arithmetic properties of periodic points of quadratic maps, Acta Arith. 62 (1992), 343-372.
• [m2] P. Morton, Characterizing cyclic cubic extensions by automorphism polynomials, J. Number Theory 49 (1994), 183-208.
• [m3] P. Morton, On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319-350.
• [mp] P. Morton and P. Patel, The Galois theory of periodic points of polynomial maps, Proc. London Math. Soc. 68 (1994), 225-263.
• [ms] P. Morton and J. Silverman, Periodic points, multiplicities and dynamical units, J. Reine Angew. Math. 461 (1995), 81-122.
• [mv] P. Morton and F. Vivaldi, Bifurcations and discriminants for polynomial maps, Nonlinearity 8 (1995), 571-584.
• [rw] P. Russo and R. Walde, Rational periodic points of the quadratic function $Q_c(x) = x² + c$, Amer. Math. Monthly 101 (1994), 318-331.
• [tvw] E. Thiran, D. Verstegen and J. Weyers, p-adic dynamics, J. Statist. Phys. 54 (1989), 893-913.
• [vh1] F. Vivaldi and S. Hatjispyros, Galois theory of periodic orbits of rational maps, Nonlinearity 5 (1992), 961-978.
• [vh2] F. Vivaldi and S. Hatjispyros, A family of rational zeta functions for the quadratic map, Nonlinearity 8 (1995), 321-332.
• [w1] L. Washington, A family of cyclic quartic fields arising from modular curves, Math. Comp. 57 (1991), 763-775.
• [w2] L. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.