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Arithmetic of Polynomial Dynamical Pairs

English

By (author): Charles Favre Thomas Gauthier

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.

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€192.20
A01=Charles FavreA01=Thomas GauthierAffine transformationAge Group_UncategorizedAlgebraic closureAlgebraic curveAlgebraic equationAlgebraic extensionAlgebraic surfaceAlgebraic varietyAlgebraically closed fieldAnalytic functionAnalytic geometryArithmetic dynamicsAuthor_Charles FavreAuthor_Thomas Gauthierautomatic-updateBall (mathematics)Bifurcation theoryCantor setCategory1=Non-FictionCategory=PBCategory=PBMWCategory=PHDCategory=PHDTCharacterization (mathematics)Chebyshev polynomialsCoefficientCombinatoricsComplex numberComputationComputer programmingConnected component (graph theory)Continuous function (set theory)COP=United StatesCoprime integersCorrespondence theorem (group theory)Critical graphDatasheetDelivery_Delivery within 10-20 working daysDisk (mathematics)Divisor (algebraic geometry)eq_isMigrated=2eq_non-fictioneq_scienceEquidistribution theoremEquivalence relationExistential quantificationFixed point (mathematics)Function spaceGraph (discrete mathematics)Hausdorff measureHolomorphic functionInstance (computer science)Intermediate value theoremIntersection (set theory)Inverse-square lawIrreducible componentJordan curve theoremJulia setLanguage_EnglishLine (geometry)Moduli spaceMoment (mathematics)Montel's theoremPA=AvailableParameterPascal's WagerPolynomialPower seriesPrice_€100 and abovePrimitive polynomial (field theory)PS=ActiveQuotient ringRealizabilityRiemann surfaceRing of integersSet (mathematics)Sheaf (mathematics)Sign (mathematics)softlaunchStone–Weierstrass theoremSubharmonic functionSupport (mathematics)Surjective functionTheoremTheoryTopologyVariable (computer science)Variable (mathematics)Zariski topology
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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.

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