2010/10/04 by Thomas Scanlon, Scanlon, Thomas
Mathematics · #03C64 #14G #37P10 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #math.AG #math.DS #math.LO #math.NT #msc:03C64 #msc:14G #msc:37P10
paper · pdf · doi:10.48550/arxiv.1010.0482
arxiv created 2010/10/04 · arxiv updated 2010/10/05
Using the theory of o-minimality we show that the p-adic method of Skolem-Mahler-Lech-Chabauty may be adapted to prove instances of the dynamical Mordell-Lang conjecture for some real analytic dynamical systems. For example, we show that if f1,...,fn is a finite sequence of real analytic functions fi:(-1,1) → (-1,1) for which fi(0) = 0 and |fi'(0)| ≤ 1 (possibly zero), a = (a1,...,an) is an n-tuple of real numbers close enough to the origin and H(x1,...,xn) is a real analytic function of n variables, then the set \m ∈ \mathbb N : H (f1∘ m (a1),...,fn∘ m(an)) = 0 \ is either all of \mathbb N, all of the odd numbers, all of the even numbers, or is finite.