an:05859979
Zbl 1214.11070
Ih, Su-Ion
A nondensity property of preperiodic points on Chebyshev dynamical systems
EN
J. Number Theory 131, No. 4, 750-780 (2011).
0022-314X 1096-1658
2011
j
37P15 11G05 11G35 11J71 14G05 37P30 37P35
canonical measures; Chebyshev polynomials; equidistribution; height; integral points; preperiodic points
Summary: Let \(k\) be a number field with algebraic closure \(\overline{k}\), and let \(S\) be a finite set of primes of \(k\), containing all the infinite ones. Consider a Chebyshev dynamical system on \({\mathbb P}^2\). Fix the effective divisor \(D\) of \({\mathbb P}^2\) that is equal to a line nondegenerate on \([-2,2]^2\). Then we prove that the set of preperiodic points on \({\mathbb P}^2(\overline{k})\) which are \(S\)-integral relative to \(D\) is not Zariski dense in \({\mathbb P}^2 \).