A gap principle for dynamics

Author:

Benedetto Robert L.,Ghioca Dragos,Kurlberg Pär,Tucker Thomas J.

Abstract

AbstractLet f1,…,fg∈ℂ(z) be rational functions, let Φ=(f1,…,fg) denote their coordinate-wise action on (ℙ1)g, let V ⊂(ℙ1)g be a proper subvariety, and let P be a point in (ℙ1)g(ℂ). We show that if 𝒮={n≥0:Φn(P)∈V (ℂ)} does not contain any infinite arithmetic progressions, then 𝒮 must be a very sparse set of integers. In particular, for any k and any sufficiently large N, the number of nN such that Φn(P)∈V (ℂ) is less than log kN, where log k denotes the kth iterate of the log function. This result can be interpreted as an analogue of the gap principle of Davenport–Roth and Mumford.

Publisher

Wiley

Subject

Algebra and Number Theory

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Unlikely intersections on the p-adic formal ball;Research in Number Theory;2023-04-30

2. On semigroup orbits of polynomials in multiplicative subgroups;Monatshefte für Mathematik;2021-11-17

3. On intersections of polynomial semigroups orbits with plane lines;Canadian Mathematical Bulletin;2020-07-17

4. A Gap Principle for Subvarieties with Finitely Many Periodic Points;Canadian Mathematical Bulletin;2020-02-28

5. Dynamical Uniform Bounds for Fibers and a Gap Conjecture;International Mathematics Research Notices;2019-11-15

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