A01=Charles Favre
A01=Thomas Gauthier
Affine transformation
Age Group_Uncategorized
Age Group_Uncategorized
Algebraic closure
Algebraic curve
Algebraic equation
Algebraic extension
Algebraic surface
Algebraic variety
Algebraically closed field
Analytic function
Analytic geometry
Arithmetic dynamics
Author_Charles Favre
Author_Thomas Gauthier
automatic-update
Ball (mathematics)
Bifurcation theory
Cantor set
Category1=Non-Fiction
Category=PB
Category=PBMW
Category=PHD
Category=PHDT
Characterization (mathematics)
Chebyshev polynomials
Coefficient
Combinatorics
Complex number
Computation
Computer programming
Connected component (graph theory)
Continuous function (set theory)
COP=United States
Coprime integers
Correspondence theorem (group theory)
Critical graph
Datasheet
Delivery_Delivery within 10-20 working days
Disk (mathematics)
Divisor (algebraic geometry)
eq_isMigrated=2
eq_non-fiction
eq_science
Equidistribution theorem
Equivalence relation
Existential quantification
Fixed point (mathematics)
Function space
Graph (discrete mathematics)
Hausdorff measure
Holomorphic function
Instance (computer science)
Intermediate value theorem
Intersection (set theory)
Inverse-square law
Irreducible component
Jordan curve theorem
Julia set
Language_English
Line (geometry)
Moduli space
Moment (mathematics)
Montel's theorem
PA=Available
Parameter
Pascal's Wager
Polynomial
Power series
Price_€100 and above
Primitive polynomial (field theory)
PS=Active
Quotient ring
Realizability
Riemann surface
Ring of integers
Set (mathematics)
Sheaf (mathematics)
Sign (mathematics)
softlaunch
Stone–Weierstrass theorem
Subharmonic function
Support (mathematics)
Surjective function
Theorem
Theory
Topology
Variable (computer science)
Variable (mathematics)
Zariski topology
Arithmetic of Polynomial Dynamical Pairs
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.
See more
Product Details
- Dimensions: 156 x 235mm
- Publication Date: 14 Jun 2022
- Publisher: Princeton University Press
- Publication City/Country: US
- Language: English
- ISBN13: 9780691235462
About Charles FavreThomas Gauthier
Charles Favre is a CNRS senior researcher based at the École Polytechnique in Paris. He is the coauthor of The Valuative Tree and the coeditor of Berkovich Spaces and Applications. Thomas Gauthier is professor of mathematics at the Université Paris-Saclay.