Dynamical Mordell-Lang conjecture / Jason P. Bell, Dragos Ghioca and Thomas J. Tucker.
Material type:
TextSeries: Mathematical surveys and monographs ; v 210.Publication details: Providence : American Mathematical Society, ©2016.Description: xiii, 280 pages ; 26 cmISBN: - 9781470424084
- 510MS 23 Am512
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 510MS Am512 (Browse shelf(Opens below)) | Available | 137673 |
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| 510MS Am512 Asymptotic geometric analysis / | 510MS Am512 Foundation for PROPs, algebras, and modules / | 510MS Am512 Toric topology / | 510MS Am512 Dynamical Mordell-Lang conjecture / | 510MS Am512 Galois theories of linear difference equations : an introduction / | 510MS Am512 Ramsey theory for product spaces / | 510MS Am512 Beurling generalized numbers / |
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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