TY  - BOOK
AU  - Bell,Jason P.
AU  - Ghioca,Dragos
AU  - Tucker,Thomas J.
TI  - Dynamical Mordell-Lang conjecture
T2  - Mathematical surveys and monographs
SN  - 9781470424084 
U1  - 510MS 23
PY  - 2016///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Mordell conjecture
KW  - Algebraic curves
KW  - Arithmetical algebraic geometry
KW  - Algebraic geometry
N1  - Includes bibliographical references and index; 1. Introduction --
2. Background material --
3. The dynamical mordell-lang problem --
4. A geometric Skolem-Mahler-Lech theorem --
5. Linear relations between points in polynomial orbits --
6. Parameterization of orbits --
7. The split case in the dynamical mordell-ang conjecture --
8. Heuristics for avoiding ramification --
9. Higher dimensional results --
10. Additional results towards the dynamical mordell-lang conjecture --
11. Sparse sets in the dynamical mordell-lang conjecture --
12. Denis-mordell-lang conjecture --
13. Dynamical mordell-lang conjecture in positive characteristic --
14. Related problems in arithmetic dynamics --
15. Future directions
N2  - 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
ER  -