The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture within the context of mathematics dynamics. It predicts the habit of the orbit of some extent $x$ less than the motion of an endomorphism $f$ of a quasiprojective advanced kind $X$. extra accurately, it claims that for any element $x$ in $X$ and any subvariety $V$ of $X$, the set of indices $n$ such that the $n$-th iterate of $x$ less than $f$ lies in $V$ is a finite union of mathematics progressions. during this booklet the authors current all recognized effects concerning the Dynamical Mordell-Lang Conjecture, focusing as a rule on a $p$-adic technique which gives a parametrization of the orbit of some degree below an endomorphism of a range.

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