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I recently attended a webinar where the speaker was introducing some research topics to the audience. There I was introduced to Arithmetic Dynamics and found it to be an interesting topic. I wish to learn it but I'm not sure I should start right away. I have taken the standard courses on algebra, topology and analysis. I also had Hyperbolic Geometry and Complex Dynamics as my elective courses. Are these enough or do I have to read some more stuff? Are there any standard textbooks to which I should refer?

J W
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Ajin Shaji Jose
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  • See also my answer https://math.stackexchange.com/a/1971588/118539, in which I also list some resources. – J W Dec 31 '24 at 20:28

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Definitely "The arithmetic of Dynamical Systems" by Silverman is THE textbook you should read first.

In my opinion, in order to get a grasp of what arithmetic dynamics is about, you firstly need solid bases of algebraic geometry and number theory. Complex dynamics is also going to be pretty helpful if you want to enter the more dynamical aspects of the theory.

Ferra
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  • Agree wholeheartedly here with the recommendation of Silverman's book. And follow up with Benedetto's Dynamics in One Non-Archimedean Variable if that sub-area interests you. – J W Dec 31 '24 at 20:38