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Current trends and open problems in arithmetic dynamics


Authors: Robert Benedetto, Patrick Ingram, Rafe Jones, Michelle Manes, Joseph H. Silverman and Thomas J. Tucker
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
Published electronically: March 1, 2019
MathSciNet review: 4007163
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Abstract | References | Similar Articles | Additional Information

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

Keywords: Arithmetic dynamics, open problems
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.
Article copyright: © Copyright 2019 American Mathematical Society