The Arithmetic of Dynamical Systems

By Joseph H. Silverman. 2007

742 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/25294be71fa560b92a674213addf704c19361a18

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Citations in the corpus

Difference fields and descent in algebraic dynamics. I (2007, background): “mple divisor, his “proper” in the sense that the inverse image of a bounded subset of E∗ is a limited subset of V(Kalg). Proof. Recall the lemma behind Tate’s canonical heights construction (cf. e.g. [25] Theorem 3.20). let Xbe a set, T: X→ Xa function, h: X→ R, λ∈ R,λ>1. Suppose h◦T−λh is a boun”
ON MINIMAL DECOMPOSITION OF p-ADIC POLYNOMIAL DYNAMICAL SYSTEMS (2010, background): “See also the monographes [5], [25], [36] and the bibliographies therein.”
Galois theory of quadratic rational functions (2011, background): “q; p/, then has good reduction at `, and thus so do all iterates of [17], Theorem 2.”
Bifurcation Currents in Holomorphic Families of Rational Maps (2012, methodology): “2;C/ is not free, it may be proven that Modd is a normal quasi-projective variety [59].”
Dynamics on Berkovich Spaces in Low Dimensions (2012, background): “nd properties of wandering components etc. See [BR10, x10] and [Ben10, xx6{7] for this. Finally, we have said nothing at all about arithmetic aspects of dynamical systems. For this, see e.g. the book [Sil07] and lecture notes [Sil10] by Silverman. 68 MATTIAS JONSSON 6. The Berkovich affine plane ove”
Invariant varieties for polynomial dynamical systems (2009, background): “6 of [19]), we see that C = P1 and either h and γ are polynomials, or S has exactly two elements and (P1, h) is isomorphic to (P1, x 7→ 1 xdeg(f) ).”
Distribution of postcritically finite polynomials (2013, neutral): “In this section, we explain how to parameterize the set of polynomials P ∈ Polyd possessing a cycle with a given multiplier and period following [S] and [BB3, §2.”
Bifurcations, intersections, and heights (2014, background): “MR 1312368 Zbl 0911.14015 [Silverman 2007] J. H. Silverman, The arithmetic of dynamical systems, Graduate Texts in Mathematics 241, Springer, New York, 2007.”