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A gap principle for dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2010 (English)In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 146, no 4, 1056-1072 p.Article in journal (Refereed) Published
Abstract [en]

Let f(1), ... , f(g) is an element of C(z) be rational functions, let Phi = (f(1), ... ,f(g)) denote their coordinate-wise action on (P-1)(g), let V subset of (P-1)(g) be a proper subvariety, and let P be a point in (P-1)(g)(C). We show that if S = {n >= 0 : Phi(n)(P) is an element of 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 n <= N such that Phi(n)(P) is an element of V(C) is less than log(k)N, 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-koth and Mumford.

Place, publisher, year, edition, pages
2010. Vol. 146, no 4, 1056-1072 p.
Keyword [en]
p-adic dynamics, Mordell-Lang conjecture
National Category
URN: urn:nbn:se:kth:diva-29446DOI: 10.1112/S0010437X09004667ISI: 000280156000010ScopusID: 2-s2.0-77957223719OAI: diva2:396191
Knut and Alice Wallenberg FoundationSwedish Research Council
QC 20110209Available from: 2011-02-09 Created: 2011-02-02 Last updated: 2012-04-14Bibliographically approved

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Kurlberg, Pär
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