Related papers: Birational maps with transcendental dynamical degr…

We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional…

We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics…

We prove a refined version of Markov's theorem in Diophantine approximation. More precisely, we characterize completely the set of irrationals $x$ such that $\left|x-\frac{p}{q}\right|<\frac{1}{3q^2}$ has only finitely many rational…

For an invariant probability measure for the Gauss map, almost all numbers are Diophantine if the log of the partial quotient function is integrable. We show that with respect to a ``continued fraction mixing'' measure for the Gauss map…

We consider the dynamical properties of transcendental entire functions and their compositions. We give several conditions under which Fatou set of a transcendental entire function $f$ coincide with that of $f\circ g,$ where $g$ is another…

A geometric realization of a birational map $\psi$ among two complex projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action inducing $\psi$ as the natural birational map among two extremal geometric quotients. In this…

Let xi be a real number which is neither rational nor quadratic over Q. Based on work of Davenport and Schmidt, Bugeaud and Laurent have shown that, for any real number theta, there exist a constant c>0 and infinitely many non-zero…

We introduce an algebraic formulation of billiards on plane curves over algebraically closed fields, extending Glutsyuk's complex billiards. For any smooth algebraic curve $C$ of degree $d \geq 2$, algebraic billiards is a rational…

The study of the dynamics of polynomials is now a major field of research, with many important and elegant results. The study of entire functions that are not polynomials -- in other words transcendental entire functions -- is somewhat less…

We derive a formula for the generating function of d-irreducible bipartite planar maps with several boundaries, i.e. having several marked faces of controlled degrees. It extends a formula due to Collet and Fusy for the case of arbitrary…

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=\sum_{i=1}^n d(G,i) x^i$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. The $n$-barbell graph $Bar_n$ with $2n$…

We discuss here a generalization of a theorem by Dunfield stating that the peripheral holonomy map, from the character variety of a 3-manifold to the A-polynomial is birational. Dunfield's proof involves the rigidity of maximal volume. The…

We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…

Chen et al. recently established bijections for $(d+1)$-noncrossing/ nonnesting matchings, oscillating tableaux of bounded height $d$, and oscillating lattice walks in the $d$-dimensional Weyl chamber. Stanley asked what is the total number…

Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…

The article revisits birational and biregular automorphisms of the Hilbert scheme of points on a K3 surface from the perspective of derived categories. Under the assumption that the K3 surface is generic, the birational and biregular…

We study one-dimensional algebraic families of pairs given by a polynomial with a marked point. We prove an "unlikely intersection" statement for such pairs thereby exhibiting strong rigidity features for these pairs. We infer from this…

Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…

One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…

We prove some asymptotic results for the radius and the profile of large random rooted planar maps with faces of arbitrary degrees. Using a bijection due to Bouttier, Di Francesco and Guitter between rooted planar maps and certain four-type…