The Arithmetic of Polynomial Dynamical Pairs

By Thomas Gauthier and Charles Favre

New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs , Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an "unlikely intersection" statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.

• Format: Paperback
• Language: English
• ISBN: 0691235473
• ISBN13: 9780691235479
• Release Date: June 2022
• Publisher: Princeton University Press
• Length: 252 Pages
• Weight: 0.80 lbs.
• Dimensions: 0.7" x 9.1" x 6.1"