منابع مشابه
Preperiodic points for families of rational maps
Let X be a smooth curve defined over Q̄, let a, b ∈ P(Q̄) and let fλ(x) ∈ Q̄(x) be an algebraic family of rational maps indexed by all λ ∈ X(C). We study whether there exist infinitely many λ ∈ X(C) such that both a and b are preperiodic for fλ. In particular, we show that if P,Q ∈ Q̄[x] such that deg(P ) 2 + deg(Q), and if a, b ∈ Q̄ such that a is periodic for P (x)/Q(x), but b is not preperiodic f...
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Let F be a family of holomorphic functions and suppose that there exists ε > 0 such that if f ∈ F , then |(f2)′(ξ)| ≤ 4 − ε for all fixed points ξ of the second iterate f. We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p has a fixed point ξ such that |(p2)′(ξ)| ≥ 4. The results are motivated by a problem posed by Yang...
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Let Φ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for Φ for all λ. If there exist infinitely many λ ∈ K such that both a(λ) and b(λ) are torsion points for Φ, then we show that for each λ ∈ K, we have that a(λ) is torsion for Φ if and only if b(λ) is torsion for Φ. In the case a,b...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.2307/2047153