Exponential-polynomial equations and dynamical return sets

Thomas Scanlon, Yu Yasufuku

We show that for each finite sequence of algebraic integers ${\alpha }_1,...,{\alpha }_n$ and polynomials $P_1(x_1,...,x_n;y_1,...,y_n),...,P_r(x_1,...,x_n;y_1,...,y_n)$ with algebraic integer co…