The Arithmetic of Polynomial Dynamical Pairs : : (AMS-214) / / Charles Favre, Thomas Gauthier.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2022 English
• VerfasserIn: Favre, Charles,; Gauthier, Thomas,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: Annals of Mathematics Studies ; 214
• Physical Description: 1 online resource (252 p.) :; 18 b/w illus.
• Other title: Frontmatter --; Contents --; List of figures --; Preface --; List of abbreviations --; Introduction --; Chapter One. Geometric background --; Chapter Two. Polynomial dynamics --; Chapter Three. Dynamical symmetries --; Chapter Four. Polynomial dynamical pairs --; Chapter Five. Entanglement of dynamical pairs --; Chapter Six. Entanglement of marked points --; Chapter Seven. The unicritical family --; Chapter Eight. Special curves in the parameter space of polynomials --; Notes --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9780691235486; 9783110993899; 9783110994810; 9783110993868; 9783110770445; 9783110749731
• DOI: 10.1515/9780691235486?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Charles Favre, Thomas Gauthier.

New mathematical research in arithmetic dynamicsIn 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.