Power maps and subvarieties of the complex algebraic $n$--torus

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dc.creatorAliev, Iskander
dc.creatorSmyth, Chris
dc.date2008-02-20
dc.date2008-04-27
dc.date.accessioned2026-07-07T09:35:09Z
dc.date.available2026-07-07T09:35:09Z
dc.descriptionGiven a subvariety $V$ of the complex algebraic torus ${\mathbb G}_{\rm m}^n$ defined by polynomials of total degree at most $d$ and a power map $ϕ: {\mathbb G}_{\rm m}^n \to {\mathbb G}_{\rm m}^n$, the points ${\bf x}$ whose forward orbits ${\mathcal O}_ϕ({\bf x})$ belong to $V$ form its {\em stable} subvariety $S(V,ϕ)$. The main result of the paper provides an upper bound $T=T(n,d,ϕ)$ for the number of iterations of the power map $ϕ$ required to ``cut off'' the points of $V$ that do not belong to $S$.
dc.description12 pages, corrected typos
dc.identifierhttps://arxiv.org/abs/0802.2938
dc.identifierhttp://arxiv.org/abs/0802.2938
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159738
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.subject11G35; 14L40
dc.titlePower maps and subvarieties of the complex algebraic $n$--torus
dc.typetext

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