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- Arithmetic_dynamics abstract "Arithmetic dynamics is 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 which one 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 wikiPageLength "14331".
- Arithmetic_dynamics wikiPageOutDegree "45".
- Arithmetic_dynamics wikiPageRevisionID "694237405".
- Arithmetic_dynamics wikiPageWikiLink Abelian_variety.
- Arithmetic_dynamics wikiPageWikiLink Arithmetic_of_abelian_varieties.
- Arithmetic_dynamics wikiPageWikiLink Arithmetic_topology.
- Arithmetic_dynamics wikiPageWikiLink Berkovich_space.
- Arithmetic_dynamics wikiPageWikiLink Birch_and_Swinnerton-Dyer_conjecture.
- Arithmetic_dynamics wikiPageWikiLink Bjorn_Poonen.
- Arithmetic_dynamics wikiPageWikiLink Category:Algebraic_number_theory.
- Arithmetic_dynamics wikiPageWikiLink Category:Dynamical_systems.
- Arithmetic_dynamics wikiPageWikiLink Collatz_conjecture.
- Arithmetic_dynamics wikiPageWikiLink Combinatorics_and_dynamical_systems.
- Arithmetic_dynamics wikiPageWikiLink Complex_plane.
- Arithmetic_dynamics wikiPageWikiLink Diophantine_equation.
- Arithmetic_dynamics wikiPageWikiLink Drinfeld_module.
- Arithmetic_dynamics wikiPageWikiLink Dynamical_system.
- Arithmetic_dynamics wikiPageWikiLink Equidistributed_sequence.
- Arithmetic_dynamics wikiPageWikiLink Faltingss_theorem.
- Arithmetic_dynamics wikiPageWikiLink Finite_field.
- Arithmetic_dynamics wikiPageWikiLink Gerd_Faltings.
- Arithmetic_dynamics wikiPageWikiLink Global_field.
- Arithmetic_dynamics wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
- Arithmetic_dynamics wikiPageWikiLink Integer_lattice.
- Arithmetic_dynamics wikiPageWikiLink Iterated_function.
- Arithmetic_dynamics wikiPageWikiLink Joseph_H._Silverman.
- Arithmetic_dynamics wikiPageWikiLink Joseph_Silverman.
- Arithmetic_dynamics wikiPageWikiLink Julia_set.
- Arithmetic_dynamics wikiPageWikiLink Lie_group.
- Arithmetic_dynamics wikiPageWikiLink Measure_(mathematics).
- Arithmetic_dynamics wikiPageWikiLink Moduli_space.
- Arithmetic_dynamics wikiPageWikiLink Number_theory.
- Arithmetic_dynamics wikiPageWikiLink P-adic_dynamics.
- Arithmetic_dynamics wikiPageWikiLink P-adic_number.
- Arithmetic_dynamics wikiPageWikiLink Patrick_Morton.
- Arithmetic_dynamics wikiPageWikiLink Periodic_point.
- Arithmetic_dynamics wikiPageWikiLink Polynomial.
- Arithmetic_dynamics wikiPageWikiLink Power_series.
- Arithmetic_dynamics wikiPageWikiLink Projective_variety.
- Arithmetic_dynamics wikiPageWikiLink Rational_function.
- Arithmetic_dynamics wikiPageWikiLink Rational_point.
- Arithmetic_dynamics wikiPageWikiLink Real_line.
- Arithmetic_dynamics wikiPageWikiLink Robert_L._Benedetto.
- Arithmetic_dynamics wikiPageWikiLink Shou-Wu_Zhang.
- Arithmetic_dynamics wikiPageWikiLinkText "Arithmetic dynamics".
- Arithmetic_dynamics wikiPageWikiLinkText "Global arithmetic dynamics".
- Arithmetic_dynamics wikiPageWikiLinkText "Nonarchimedean dynamics".
- Arithmetic_dynamics wikiPageWikiLinkText "algebraic dynamical system".
- Arithmetic_dynamics wikiPageWikiLinkText "arithmetic dynamics".
- Arithmetic_dynamics wikiPageUsesTemplate Template:=.
- Arithmetic_dynamics wikiPageUsesTemplate Template:Math.
- Arithmetic_dynamics wikiPageUsesTemplate Template:Mvar.
- Arithmetic_dynamics wikiPageUsesTemplate Template:Number_theory-footer.
- Arithmetic_dynamics wikiPageUsesTemplate Template:Reflist.
- Arithmetic_dynamics subject Category:Algebraic_number_theory.
- Arithmetic_dynamics subject Category:Dynamical_systems.
- Arithmetic_dynamics hypernym Field.
- Arithmetic_dynamics type Field.
- Arithmetic_dynamics type Mechanic.
- Arithmetic_dynamics type Physic.
- Arithmetic_dynamics comment "Arithmetic dynamics is 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 sameAs Q4791123.
- Arithmetic_dynamics sameAs 数論力学.
- Arithmetic_dynamics sameAs m.0463skm.
- Arithmetic_dynamics sameAs Q4791123.
- Arithmetic_dynamics wasDerivedFrom Arithmetic_dynamics?oldid=694237405.
- Arithmetic_dynamics isPrimaryTopicOf Arithmetic_dynamics.