The Arithmetic of Dynamical Systems

Joseph H. Silverman

Springer-Verlag – Graduate Texts in Mathematics 241
ISBN: 13: 978-0-387-69903-5 – 1st ed. – © 2007 – 511 + ix pages
Math. Subj. Class [2010]: 37Pxx (37P05, 37P15, 37P20, 37P30, 37P35, 37P45, 37P50)
Available from Amazon and direct from Springer.

The Arithmetic of Dynamical Systems is a graduate level text designed to provide an entry into a new field that is an amalgamation of two venerable areas of mathematics, Dynamical Systems and Number Theory. Many of the motivating theorems and conjectures in the new subject of Arithmetic Dynamics may be viewed as the transposition of classical results in the theory of Diophantine equations to the setting of discrete dynamical systems, especially to the iteration theory of maps on the projective line and other algebraic varieties.


  1. An Introduction to Classical Dynamics
  2. Dynamics Over Local Fields: Good Reduction
  3. Dynamics Over Global Fields
  4. Families of Dynamical Systems
  5. Dynamics Over Local Fields: Bad Reduction
  6. Dynamics Associated to Algebraic Groups
  7. Dynamics in Dimension Greater Than One

Click on the links for the following material.

Errata List

Contact Information

No book is ever free from error or incapable of being improved. I would be delighted to receive comments, good or bad, and corrections from my readers. You can send mail to me at

Return to Top of Page.
Go to J.H. Silverman's Home Page .