The dynamical Mordell-Lang problem for Noetherian spaces
نویسندگان
چکیده
منابع مشابه
The Dynamical Mordell-lang Problem for Noetherian Spaces
Let X be a Noetherian space, let Φ : X −→ X be a continuous function, let Y ⊆ X be a closed set, and let x ∈ X. We show that the set S := {n ∈ N : Φn(x) ∈ Y } is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety X, any rational map Φ : X −→ X, any subvariety Y ⊆ X, and any point x ∈ ...
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Article history: Received 11 May 2008 Revised 20 September 2008 Available online 28 November 2008 Communicated by S.-W. Zhang MSC: primary 14K12 secondary 37F10
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Let k be an algebraically closed field of characteristic 0, let N ∈ N, let g : P−→P be a non-constant morphism, and let A : A−→A be a linear transformation defined over k(P), i.e., for a Zariski open dense subset U ⊂ P, we have that for x ∈ U(k), the specialization A(x) is an N -by-N matrix with entries in k. We let f : P×A99KP×A be the rational endomorphism given by (x, y) 7→ (g(x), A(x)y). We...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2015
ISSN: 0208-6573
DOI: 10.7169/facm/2015.53.2.7