The Arithmetic of Polynomial Dynamical Pairs : : (AMS-214) /

The Arithmetic of Polynomial Dynamical Pairs : : (AMS-214) / / 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...

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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
Online Access:
Physical Description:1 online resource (252 p.) :; 18 b/w illus.
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245 1 4 |a The Arithmetic of Polynomial Dynamical Pairs :  |b (AMS-214) /  |c Charles Favre, Thomas Gauthier. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2022] 
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490 0 |a Annals of Mathematics Studies ;  |v 214 
505 0 0 |t Frontmatter --   |t Contents --   |t List of figures --   |t Preface --   |t List of abbreviations --   |t Introduction --   |t Chapter One. Geometric background --   |t Chapter Two. Polynomial dynamics --   |t Chapter Three. Dynamical symmetries --   |t Chapter Four. Polynomial dynamical pairs --   |t Chapter Five. Entanglement of dynamical pairs --   |t Chapter Six. Entanglement of marked points --   |t Chapter Seven. The unicritical family --   |t Chapter Eight. Special curves in the parameter space of polynomials --   |t Notes --   |t Bibliography --   |t Index 
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520 |a 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. 
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546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Mai 2023) 
650 7 |a MATHEMATICS / Geometry / Algebraic.  |2 bisacsh 
653 |a Affine plane. 
653 |a Affine space. 
653 |a Affine transformation. 
653 |a Algebraic closure. 
653 |a Algebraic curve. 
653 |a Algebraic equation. 
653 |a Algebraic extension. 
653 |a Algebraic surface. 
653 |a Algebraic variety. 
653 |a Algebraically closed field. 
653 |a Analysis. 
653 |a Analytic function. 
653 |a Analytic geometry. 
653 |a Approximation. 
653 |a Arithmetic dynamics. 
653 |a Asymmetric graph. 
653 |a Ball (mathematics). 
653 |a Bifurcation theory. 
653 |a Boundary (topology). 
653 |a Cantor set. 
653 |a Characterization (mathematics). 
653 |a Chebyshev polynomials. 
653 |a Coefficient. 
653 |a Combinatorics. 
653 |a Complex manifold. 
653 |a Complex number. 
653 |a Computation. 
653 |a Computer programming. 
653 |a Conjugacy class. 
653 |a Connected component (graph theory). 
653 |a Continuous function (set theory). 
653 |a Coprime integers. 
653 |a Correspondence theorem (group theory). 
653 |a Counting. 
653 |a Critical graph. 
653 |a Cubic function. 
653 |a Datasheet. 
653 |a Disk (mathematics). 
653 |a Divisor (algebraic geometry). 
653 |a Elliptic curve. 
653 |a Equation. 
653 |a Equidistribution theorem. 
653 |a Equivalence relation. 
653 |a Euclidean topology. 
653 |a Existential quantification. 
653 |a Fixed point (mathematics). 
653 |a Function space. 
653 |a Geometric (company). 
653 |a Graph (discrete mathematics). 
653 |a Hamiltonian mechanics. 
653 |a Hausdorff dimension. 
653 |a Hausdorff measure. 
653 |a Holomorphic function. 
653 |a Inequality (mathematics). 
653 |a Instance (computer science). 
653 |a Integer. 
653 |a Intermediate value theorem. 
653 |a Intersection (set theory). 
653 |a Inverse-square law. 
653 |a Irreducible component. 
653 |a Iteration. 
653 |a Jordan curve theorem. 
653 |a Julia set. 
653 |a Limit of a sequence. 
653 |a Line (geometry). 
653 |a Metric space. 
653 |a Moduli space. 
653 |a Moment (mathematics). 
653 |a Montel's theorem. 
653 |a P-adic number. 
653 |a Parameter. 
653 |a Pascal's Wager. 
653 |a Periodic point. 
653 |a Polynomial. 
653 |a Power series. 
653 |a Primitive polynomial (field theory). 
653 |a Projective line. 
653 |a Quotient ring. 
653 |a Rational number. 
653 |a Realizability. 
653 |a Renormalization. 
653 |a Riemann surface. 
653 |a Ring of integers. 
653 |a Scientific notation. 
653 |a Set (mathematics). 
653 |a Sheaf (mathematics). 
653 |a Sign (mathematics). 
653 |a Stone–Weierstrass theorem. 
653 |a Subharmonic function. 
653 |a Support (mathematics). 
653 |a Surjective function. 
653 |a Theorem. 
653 |a Theory. 
653 |a Topology. 
653 |a Transfer principle. 
653 |a Union (set theory). 
653 |a Unit disk. 
653 |a Variable (computer science). 
653 |a Variable (mathematics). 
653 |a Zariski topology. 
700 1 |a Gauthier, Thomas,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
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