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Arithmetic dynamics

Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational…

Art, Other areas in which number theory and dynamics interact & Overview

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Other areas in which number theory and dynamics interact

Finite fieldsFunction fieldsPower seriesLie groupsModuli spaces
9 related topics

Overview

Dynamical systemsNumber theoryComplex dynamicsIterationComplex plane
16 related topics

Dynamically defined points lying on subvarieties

Shouwu ZhangManin–Mumford conjectureMichel RaynaudMordell–Lang conjectureGerd Faltings
5 related topics

Number theoretic properties of preperiodic points

Douglas NorthcottJoseph SilvermanConjecture of Birch and Swinnerton-DyerBjorn Poonen
4 related topics

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Overview

Number theoretic properties of preperiodic points

Dynamically defined points lying on subvarieties

P-adic dynamics

Generalizations

Other areas in which number theory and dynamics interact

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Arithmetic dynamics

Nodes43
Edges42
Triples31
Avg. degree1.95
Density0.046512
Components1

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Arithmetic dynamics

Top relations

related to Further reading · 10
Arithmetic dynamics → Arithmetic Dynamics Arizona Winter, Boris Hasselblatt, Cambridge University Press, ISBN, Joseph, Katok, Lecture Notes, March, School, SilvermanChapter
related to External links · 7
Arithmetic dynamics → Benedetto, Berkovich, Dynamical Systems, Joseph, Robert, Silverman's, The Arithmetic
related to Generalizations · 5
Arithmetic dynamics → Another, P1, PN, Qp, There
is a · 3
Arithmetic dynamics → field that amalgamates two areas of mathematics, study of analogues of classical diophantine geometry in the setting of discrete dynamical systems, study of the number-theoretic properties of integer

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Important terminology

dynamics arithmetic dynamical p-adic systems points rational number field many study preperiodic properties orbit nonarchimedean complex varieties integer polynomial map

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Arithmetic dynamicsis afield that amalgamates two areas of mathematics0.90text
Arithmetic dynamicsis astudy of the number-theoretic properties of integer0.90text
Arithmetic dynamicsis astudy of analogues of classical diophantine geometry in the setting of discrete dynamical systems0.90text
Qp or Cpinstance ofis an analogue of complex dynamics in which one replaces the complex numbers C by a p-adic field0.80text
studies chaotic behaviorinstance ofis an analogue of complex dynamics in which one replaces the complex numbers C by a p-adic field0.80text
the Fatouinstance ofis an analogue of complex dynamics in which one replaces the complex numbers C by a p-adic field0.80text
Julia sets.The following table describes a rough correspondence between Diophantine equationsinstance ofis an analogue of complex dynamics in which one replaces the complex numbers C by a p-adic field0.80text
especially abelian varietiesinstance ofis an analogue of complex dynamics in which one replaces the complex numbers C by a p-adic field0.80text
and dynamical systemsinstance ofis an analogue of complex dynamics in which one replaces the complex numbers C by a p-adic field0.80text
Arithmetic dynamicsrelated to External linksThe Arithmetic0.60section
Arithmetic dynamicsrelated to External linksDynamical Systems0.60section
Arithmetic dynamicsrelated to External linksBerkovich0.60section

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