The Dynamical Mordell-Lang Conjecture
| dc.creator | Benedetto, Robert L. | |
| dc.creator | Ghioca, Dragos | |
| dc.creator | Kurlberg, Par | |
| dc.creator | Tucker, Thomas J. | |
| dc.date | 2007-12-14 | |
| dc.date | 2009-02-06 | |
| dc.date.accessioned | 2026-07-07T12:38:02Z | |
| dc.date.available | 2026-07-07T12:38:02Z | |
| dc.description | We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let $ϕ$ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of $ϕ$ are algebraic, we show that the orbit of a point outside the union of proper preperiodic subvarieties of $(\bP^1)^g$ has only finite intersection with any curve contained in $(\bP^1)^g$. We also show that our result holds for indecomposable polynomials $ϕ$ with coefficients in $\bC$. Our proof uses results from $p$-adic dynamics together with an integrality argument. The extension to polynomials defined over $\bC$ uses the method of specializations coupled with some new results of Medvedev and Scanlon for describing the periodic plane curves under the action of $(ϕ,ϕ)$ on $\bA^2$. | |
| dc.description | 25 pages. Results strengthened to include the case of indecomposable polynomials with complex coefficients (using some recent results of Medvedev and Scanlon.) | |
| dc.identifier | https://arxiv.org/abs/0712.2344 | |
| dc.identifier | http://arxiv.org/abs/0712.2344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218616 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 14G25, 37F10 | |
| dc.title | The Dynamical Mordell-Lang Conjecture | |
| dc.type | text |