Related papers: Birational maps with transcendental dynamical degr…

We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a…

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover…

We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian…

In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…

We define arithmetical and dynamical degrees for dynamical systems with several rational maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial…

We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the (usual) motivic invariants vanish for birational…

We prove the existence of the arithmetic degree for dominant rational self-maps at any point whose orbit is generic. As a corollary, we prove the same existence for \'etale morphisms on quasi-projective varieties and any points on it. We…

When a birational surface map is expanding on cohomology there is a canonical way to associate positive closed currents to the map and its inverse. In this paper we use a version of Dirichlet energy to construct the wedge product of these…

We give a simple example of a polynomial contraction automorphism of $\mathbb C^d$, $ d\ge 3 $, with unbounded degree growth. Combined with Poincar\'e-Dulac theorem it provides an algebraic automorphism of $\mathbb C^d$, $ d\ge 3 $, which…

We study the geometry of infinite random Boltzmann planar maps with vertices of high degree. These correspond to the duals of the Boltzmann maps associated to a critical weight sequence $(q_{k})_{ k \geq 0}$ for the faces with polynomial…

A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear…

This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…

We provide a bijection between a class of 3-dimensional pattern avoiding permutations and triangle bases, special sets of integer points arising from the theory of tilings and TEP subshifts. This answers a conjecture of Bonichon and Morel.

A transcendental entire function is called criniferous if every point in its escaping set can eventually be connected to infinity by a curve of escaping points. Many transcendental entire functions with bounded singular set have this…

Continuing work begun in a previous paper, we study the real dynamics of a family of plane birational maps. This time we consider a parameter range where the real and complex dynamics are different. We show in particular that for one…

Let $d$ be a real number, let $s$ be in a fixed compact set of the strip $1/2<\sigma<1$, and let $L(s, \chi)$ be the Dirichlet $L$-function. The hypothesis is that for any real number $d$ there exist 'many' real numbers $\tau$ such that the…

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…

The relevance of the algebraic entropy in the study of birational discrete time dynamical systems highlights the need to relate it to other characteristics of these systems. In this letter, two complementary proofs are given that the…

This article discusses the recent transcendental techniques used in the proofs of the following three conjectures. (1)~The plurigenera of a compact projective algebraic manifold are invariant under holomorphic deformation. (2)~There exists…

I provide a proof of the existence of absolutely continuous invariant measures (and study their statistical properties) for multidimensional piecewise expanding systems with not necessarily bounded derivative or distortion. The proof uses…