The Dynamical Mordell-Lang Conjecture is an analogue of the
classical Mordell-Lang conjecture in the context of arithmetic
dynamics. It predicts the behavior of the orbit of a point $x$
under the action of an endomorphism $f$ of a quasiprojective
complex variety $X$. More precisely, it claims that for any point
$x$ in $X$ and any subvariety $V$ of $X$, the set of indices $n$
such that the $n$-th iterate of $x$ under $f$ lies in $V$ is a
finite union of arithmetic progressions. In this book the authors
present all known results about the Dynamical Mordell-Lang
Conjecture, focusing mainly on a $p$-adic approach which provides a
parametrization of the orbit of a point under an endomorphism of a
variety.
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