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.
About the Author
Jason P. Bell, University of Waterloo, Ontario, Canada.Dragos Ghioca, University of British Columbia, Vancouver, BC, Canada.Thomas J. Tucker, University of Rochester, NY, USA.
- Contributor: Jason P. Bell
- Imprint: American Mathematical Society
- ISBN13: 9781470424084
- Number of Pages: 280
- Packaged Dimensions: 178x254mm
- Format: Hardback
- Publisher: American Mathematical Society
- Release Date: 2016-04-30
- Series: Mathematical Surveys and Monographs
- Binding: Hardback
- Biography: Jason P. Bell, University of Waterloo, Ontario, Canada.Dragos Ghioca, University of British Columbia, Vancouver, BC, Canada.Thomas J. Tucker, University of Rochester, NY, USA.
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