Abstract
Let k be a number field with algebraic closure k ¯ , and let S be a finite set of primes of k, containing all the infinite ones. Consider a Chebyshev dynamical system on P 2 . Fix the effective divisor D of P 2 that is equal to a line nondegenerate on [ − 2 , 2 ] 2 . Then we will prove that the set of preperiodic points on P 2 ( k ¯ ) which are S-integral relative to D is not Zariski dense in P 2 .
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