Related papers: Dynamical Mordell-Lang conjecture for birational p…
In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.
We prove the dynamical Mordell-Lang conjecture for product of endomorphisms of an affine curve and a projective curve over $\overline{\mathbb{Q}}$.
We solve the dynamical Mordell-Lang conjecture for bounded-degree dynamical systems in positive characteristic. The answer in this case disproves the original version of the pDML conjecture.
We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of the affine space A^g over a p-adic field, endowed with polynomial actions on each coordinate of A^g. We use analytic methods similar to the ones employed by…
We prove a dynamical version of the Mordell-Lang conjecture in the context of Drinfeld modules. We use analytic methods similar to the ones employed by Skolem, Chabauty, and Coleman for studying diophantine equations.
We introduce a dynamical Mordell-Lang-type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this…
Using the Skolem-Mahler-Lech theorem, we prove a dynamical Mordell-Lang conjecture for semiabelian varieties.
Let K be an algebraically closed field of prime characteristic p, let X be a semiabelian variety defined over a finite subfield of K, let f be a regular self-map on X defined over K, let V be a subvariety of X defined over K, and let x be a…
There are three aims of this note. The first one is to report some advances around the dynamical Mordell-Lang (=DML) conjecture. Second, we generalize some known results. For example, the Dynamical Mordell-lang conjecture was known for…
We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical…
We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism f:X --> X. We use an analytic method based on the technique of Skolem, Mahler, and Lech,…
We solve the dynamical Mordell-Lang problem in positive characteristic for automorphisms of projective surfaces.
We prove a dynamical version of the Mordell-Lang conjecture for etale endomorphisms of quasiprojective varieties. We use p-adic methods inspired by the work of Skolem, Mahler, and Lech, combined with methods from algebraic geometry. As…
We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell-Lang…
This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.
We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.
We prove the dynamical Manin-Mumford conjecture for regular polynomial maps of A^2 and irreducible curves avoiding super-attracting orbits at infinity, over any field of characteristic 0.
We generalized several results for the arithmetic dynamics of monomial maps, including Silverman's conjectures on height growth, dynamical Mordell-Lang conjecture, and dynamical Manin-Mumford conjecture. These results are originally known…
We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let $\phi$ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of $\phi$…
We study a natural analogue of Collatz's Conjecture for polynomials over $\mathbb{F}_2$.