On the distribution of orbits in affine varieties

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/0z708z19j

Descriptions

Attribute Name	Values
Creator	Petsche, Clayton
Abstract	Given an affine variety X, a morphism ϕ:X→X, a point α∈X, and a Zariski-closed subset V of X, we show that the forward ϕ-orbit of α meets V in at most finitely many infinite arithmetic progressions, and the remaining points lie in a set of Banach density zero. This may be viewed as a weak asymptotic version of the dynamical Mordell–Lang conjecture for affine varieties. The results hold in arbitrary characteristic, and the proof uses methods of ergodic theory applied to compact Berkovich spaces. Keywords: Berkovich analytic spaces, Ergodic theory, Algebraic dynamical systems, Dynamical Mordell-Lang conjecture
Resource Type	Article
DOI	https://doi.org/10.1017/etds.2014.26
Date Available	2016-04-07T00:04:20+00:00
Date Issued	2015-10
Citation	Petsche, C. (2015). On the distribution of orbits in affine varieties. Ergodic Theory and Dynamical Systems, 35(07), 2231-2241. doi:10.1017/etds.2014.26
Journal Title	Ergodic Theory and Dynamical Systems
Journal Volume	35
Journal Issue/Number	7
Rights Statement	Copyright Not Evaluated
Publisher	Cambridge University Press
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/58640