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- Arithmetic_dynamics abstract "Arithmetic dynamicsis a field that amalgamates two areas of mathematics, dynamical systems and number theory.Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, and/or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.Global arithmetic dynamics refers to the study of analogues of classical Diophantine geometry in the setting of discrete dynamical systems, while local arithmetic dynamics, also called p-adic or nonarchimedean dynamics, is an analogue of classical dynamics in whichone replaces the complex numbers C by a p-adic field such as Qp or Cp and studies chaotic behavior and the Fatou and Julia sets.The following table describes a rough correspondence between Diophantine equations, especially abelian varieties, and dynamical systems:".
- Arithmetic_dynamics wikiPageExternalLink 0407433.
- Arithmetic_dynamics wikiPageExternalLink books?id=fGGP482b54sC.
- Arithmetic_dynamics wikiPageExternalLink ADSBIB.pdf.
- Arithmetic_dynamics wikiPageExternalLink 2010SilvermanNotes.pdf.
- Arithmetic_dynamics wikiPageExternalLink S0273-0979-08-01216-0.pdf.
- Arithmetic_dynamics wikiPageExternalLink ADSHome.html.
- Arithmetic_dynamics wikiPageID "17584701".
- Arithmetic_dynamics wikiPageRevisionID "605701449".
- Arithmetic_dynamics hasPhotoCollection Arithmetic_dynamics.
- Arithmetic_dynamics subject Category:Algebraic_number_theory.
- Arithmetic_dynamics subject Category:Dynamical_systems.
- Arithmetic_dynamics type Abstraction100002137.
- Arithmetic_dynamics type Attribute100024264.
- Arithmetic_dynamics type DynamicalSystem106246361.
- Arithmetic_dynamics type DynamicalSystems.
- Arithmetic_dynamics type PhaseSpace100029114.
- Arithmetic_dynamics type Space100028651.
- Arithmetic_dynamics comment "Arithmetic dynamicsis a field that amalgamates two areas of mathematics, dynamical systems and number theory.Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, and/or algebraic points under repeated application of a polynomial or rational function.".
- Arithmetic_dynamics label "Arithmetic dynamics".
- Arithmetic_dynamics label "数論力学".
- Arithmetic_dynamics sameAs 数論力学.
- Arithmetic_dynamics sameAs m.0463skm.
- Arithmetic_dynamics sameAs Q4791123.
- Arithmetic_dynamics sameAs Q4791123.
- Arithmetic_dynamics sameAs Arithmetic_dynamics.
- Arithmetic_dynamics wasDerivedFrom Arithmetic_dynamics?oldid=605701449.
- Arithmetic_dynamics isPrimaryTopicOf Arithmetic_dynamics.