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Dynamical Mordell-Lang conjecture / Jason P. Bell, Dragos Ghioca and Thomas J. Tucker.

By: Contributor(s): Material type: TextTextSeries: Mathematical surveys and monographs ; v 210.Publication details: Providence : American Mathematical Society, ©2016.Description: xiii, 280 pages ; 26 cmISBN:
  • 9781470424084
Subject(s): DDC classification:
  • 510MS 23 Am512
Contents:
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.
Summary: 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510MS Am512 (Browse shelf(Opens below)) Available 137673
Total holds: 0

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.

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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