Dynamical modular curves for quadratic polynomial maps
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DOI: 10.1090/tran/7474
Abstract: Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain class of dynamical analogues of classical modular curves. The… read more here.
Keywords: polynomial maps; curves quadratic; preperiodic points; dynamical modular ... See more keywords
Preperiodic points of polynomial dynamical systems over finite fields
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DOI: 10.1142/s1793042124501124
Abstract: For a prime $p$, positive integers $r,n$, and a polynomial $f$ with coefficients in $\mathbb{F}_{p^r}$, let $W_{p,r,n}(f)=f^n\left(\mathbb{F}_{p^r}\right)\setminus f^{n+1}\left(\mathbb{F}_{p^r}\right)$. As $n$ varies, the $W_{p,r,n}(f)$ partition the set of strictly preperiodic points of the dynamical system induced… read more here.
Keywords: finite fields; polynomial dynamical; dynamical systems; points polynomial ... See more keywords