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Book Review
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Book Information
Author(s):
Joseph H. Silverman
Title:
The arithmetic of dynamical systems
Additional book information:
Graduate Texts in Mathematics, 241, Springer,
New York,
2007,
x+511 pp.,
(hardcover)
US$49.95,
ISBN 0-978-387-69903-5
References:
-
- 1.
- A. Beardon,
Iteration of Rational Functions, Springer-Verlag, New York, 1991. MR 1128089 (92j:30026) - 2.
- R. Benedetto,
Reduction, dynamics, and Julia sets of rational functions, J. Number Theory 86 (2001), 175-195. MR 1813109 (2001m:11211) - 3.
- J.-P. Bézivin,
Sur les points périodiques des applications rationnelles en analyse ultramétrique, Acta Arith. 100 (2001), 63-74. MR 1864626 (2002j:37059) - 4.
- L. Carleson and T. Gamelin,
Complex Dynamics, Springer-Verlag, New York, 1991. MR 1230383 (94h:30033) - 5.
- L.-C. Hsia,
Closure of periodic points over a non-archimedean field, J. London Math. Soc. (2) 62 (2000), 685-700. MR 1794277 (2001j:11117) - 6.
- B. Mazur,
Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 33-186. MR 488287 (80c:14015) - 7.
- L. Merel,
Bournes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math. 124 (1996), 437-449. MR 1369424 (96i:11057) - 8.
- J. Milnor,
Dynamics in One Complex Variable: Introductory Lectures, 2nd ed., Vieweg, Braunschweig, 2000. MR 1721240 (2002i:37057) - 9.
- P. Morton,
Arithmetic properties of periodic points of quadratic maps, II, Acta Arith. 87 (1998), 89-102. MR 1665198 (2000c:11103) - 10.
- P. Morton and J. Silverman,
Rational periodic points of rational functions, Inter. Math. Res. Notices 2 (1994), 97-110. MR 1264933 (95b:11066) - 11.
- D. Northcott,
Periodic points of an algebraic variety, Ann. Math. 51 (1950), 167-177. MR 0034607 (11:615c) - 12.
- B. Poonen,
The classification of rational preperiodic points of quadratic polynomials over : a refined conjecture, Math. Z. 228 (1998), 11-29. MR 1617987 (99j:11076) - 13.
- J. Rivera-Letelier,
Dynamique des fonctions rationnelles sur des corps locaux, Astérisque 287 (2003), 147-230. MR 2040006 (2005f:37100) - 14.
- R. Rumely and M. Baker,
Analysis and dynamics on the Berkovich projective line, preprint, math.NT/0407433, 2004. - 15.
- J. Silverman,
The Arithmetic of Elliptic Curves, Springer-Verlag, New York, 1986. MR 817210 (87g:11070) - 16.
- J. Silverman,
Advanced Topics in the Arithmetic of Elliptic Curves, Springer-Verlag, New York, 1994. MR 1312368 (96b:11074)
Additional Information:
Reviewer(s):
Robert
L.
Benedetto
Affiliation:
Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts 01002
Email:
rlb@cs.amherst.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
46
(2009),
157-164.
MSC
(2000):
Primary 11G99;
Secondary 11D45, 37F10
DOI:
10.1090/S0273-0979-08-01216-0
PII:
S 0273-0979(08)01216-0
Posted:
August 29, 2008
Additional notes:
The reviewer gratefully acknowledges the support of NSF Grant DMS-0600878.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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