Hardcover ISBN:  9781470424084 
Product Code:  SURV/210 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Electronic ISBN:  9781470429089 
Product Code:  SURV/210.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 

Book DetailsMathematical Surveys and MonographsVolume: 210; 2016; 280 ppMSC: Primary 11; 14; 37;
The Dynamical MordellLang Conjecture is an analogue of the classical MordellLang 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 MordellLang Conjecture, focusing mainly on a \(p\)adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.
ReadershipGraduate students and research mathematicians interested in algebraic geometry and its arithmetic applications.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Background material

Chapter 3. The dynamical MordellLang problem

Chapter 4. A geometric SkolemMahlerLech theorem

Chapter 5. Linear relations between points in polynomial orbits

Chapter 6. Parametrization of orbits

Chapter 7. The split case in the dynamical MordellLang conjecture

Chapter 8. Heuristics for avoiding ramification

Chapter 9. Higher dimensional results

Chapter 10. Additional results towards the dynamical MordellLang conjecture

Chapter 11. Sparse sets in the dynamical MordellLang conjecture

Chapter 12. DenisMordellLang conjecture

Chapter 13. Dynamical MordellLang conjecture in positive characteristic

Chapter 14. Related problems in arithmetic dynamics

Chapter 15. Future directions


Additional Material

Reviews

...[S]uitable for experts working on problems related to the dynamical MordellLang conjecture. It may also be of interest to anyone who is interested in dynamics or number theory.
LiangChung Hsia, Mathematical Reviews


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The Dynamical MordellLang Conjecture is an analogue of the classical MordellLang 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 MordellLang Conjecture, focusing mainly on a \(p\)adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.
Graduate students and research mathematicians interested in algebraic geometry and its arithmetic applications.

Chapters

Chapter 1. Introduction

Chapter 2. Background material

Chapter 3. The dynamical MordellLang problem

Chapter 4. A geometric SkolemMahlerLech theorem

Chapter 5. Linear relations between points in polynomial orbits

Chapter 6. Parametrization of orbits

Chapter 7. The split case in the dynamical MordellLang conjecture

Chapter 8. Heuristics for avoiding ramification

Chapter 9. Higher dimensional results

Chapter 10. Additional results towards the dynamical MordellLang conjecture

Chapter 11. Sparse sets in the dynamical MordellLang conjecture

Chapter 12. DenisMordellLang conjecture

Chapter 13. Dynamical MordellLang conjecture in positive characteristic

Chapter 14. Related problems in arithmetic dynamics

Chapter 15. Future directions

...[S]uitable for experts working on problems related to the dynamical MordellLang conjecture. It may also be of interest to anyone who is interested in dynamics or number theory.
LiangChung Hsia, Mathematical Reviews