000			02350cam a2200301 i 4500
001			137673
003			ISI Library, Kolkata
005			20170516130047.0
008			150921s2016 riu b 001 0 eng
020			_a9781470424084
040			_aISI Library
082	0	4	_a510MS _223 _bAm512
100	1		_aBell, Jason P., _eauthor
245	1	0	_aDynamical Mordell-Lang conjecture / _cJason P. Bell, Dragos Ghioca and Thomas J. Tucker.
260			_aProvidence : _bAmerican Mathematical Society, _c©2016.
300			_axiii, 280 pages ; _c26 cm.
490	0		_aMathematical surveys and monographs ; _vv 210.
504			_aIncludes bibliographical references and index.
505	0		_a1. 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.
520			_aThe 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.
650		0	_aMordell conjecture.
650		0	_aAlgebraic curves.
650		0	_aArithmetical algebraic geometry.
650		0	_aAlgebraic geometry.
700	1		_aGhioca, Dragos, _eauthor
700	1		_aTucker, Thomas J., _eauthor
942			_2ddc _cBK
999			_c423571 _d423571