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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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Current trends and open problems in arithmetic dynamics
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by Robert Benedetto, Patrick Ingram, Rafe Jones, Michelle Manes, Joseph H. Silverman and Thomas J. Tucker PDF
Bull. Amer. Math. Soc. 56 (2019), 611-685 Request permission

Abstract:

Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry and partly from $p$-adic analogues of theorems and conjectures in classical complex dynamics. In this article we survey some of the motivating problems and some of the recent progress in the field of arithmetic dynamics.
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Additional Information
  • Robert Benedetto
  • Affiliation: Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts 01002
  • MR Author ID: 647128
  • Email: rlbenedetto@amherst.edu
  • Patrick Ingram
  • Affiliation: Department of Mathematics and Statistics, York University, N520 Ross, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
  • MR Author ID: 759982
  • Email: pingram@yorku.ca
  • Rafe Jones
  • Affiliation: Carleton College, Department of Mathematics and Statistics, Northfield, Minnesota 55057
  • MR Author ID: 676504
  • ORCID: 0000-0002-4840-4616
  • Email: rfjones@carleton.edu
  • Michelle Manes
  • Affiliation: Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, Hawaii 96822
  • MR Author ID: 838252
  • Email: mmanes@math.hawaii.edu
  • Joseph H. Silverman
  • Affiliation: Mathematics Department, Box 1917, Brown University, Providence, Rhode Island 02912
  • MR Author ID: 162205
  • ORCID: 0000-0003-3887-3248
  • Email: jhs@math.brown.edu
  • Thomas J. Tucker
  • Affiliation: Mathematics Department, 915 Hylan Building, University of Rochester, Rochester, New York 14627
  • MR Author ID: 310767
  • ORCID: 0000-0002-8582-2198
  • Email: thomas.tucker@rochester.edu
  • Received by editor(s): June 30, 2018
  • Published electronically: March 1, 2019
  • Additional Notes: The first author’s research was supported by NSF Grant DMS-1501766.
    The fourth author’s research was supported by Simons Collaboration Grant #359721.
    The fifth author’s research was supported by Simons Collaboration Grant #241309.
    The sixth author’s research was supported by NSF Grant DMS-0101636.
  • © Copyright 2019 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 56 (2019), 611-685
  • MSC (2010): Primary 37P05; Secondary 37P15, 37P20, 37P25, 37P30, 37P45, 37P55
  • DOI: https://doi.org/10.1090/bull/1665
  • MathSciNet review: 4007163