Related papers: Spectral interpretations of dynamical degrees and …

We provide a convenient framework for the study of the well-posedness of a variety of abstract (integro)differential equations in general Banach function spaces. It allows us to extend and complement the known theory on the maximal…

We provide sufficient conditions for the existence of a strong derivable map and calculate its derivative by employing a result in our previous work on strong derivability of maps arising by functional calculus of an unbounded scalar type…

We give a way to construct group of pseudo-automorphisms of rational varieties of any dimension that fix pointwise the image of a cubic hypersurface of $P^n. These group are free products of involutions, and most of their elements have…

The dynamical degrees of a rational map $f:X\dashrightarrow X$ are fundamental invariants describing the rate of growth of the action of iterates of $f$ on the cohomology of $X$. When $f$ has nonempty indeterminacy set, these quantities can…

We get three basic results in algebraic dynamics: (1). We give the first algorithm to compute the dynamical degrees to arbitrary precision. (2). We prove that for a family of dominant rational self-maps, the dynamical degrees are lower…

I compute the dynamical degrees in C. Voisin's example of a rational self-map of the variety of lines on a cubic fourfold.

The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…

We give an example of a dominant rational selfmap of the projective plane whose dynamical degree is a transcendental number.

In this paper, let k be the affine n-space over an arbitrary field k. We show that dynamical degrees of affine-triangular automorphisms in dimension 4 are algebraic integers of degree not larger than 4. As a consequence, if char(k) is not…

Let f : X --> X be a dominant rational map of a projective variety defined over a global field, let d_f be the dynamical degree of f, and let h_X be a Weil height on X relative to an ample divisor. We prove that h_X(f^n(P)) << (d_f + e)^n…

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…

A dominant rational self-map on a projective variety is called $p$-cohomologically hyperbolic if the $p$-th dynamical degree is strictly larger than other dynamical degrees. For such a map defined over $\overline{\mathbb{Q}}$, we study…

Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…

In [FJ07], Favre and Jonsson developed tools from valuative theory to study the dynamics of a dominant endomorphism of the complex affine plane. We extend this theory to the case of any affine surface, over any field. We give a new method…

The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spectral Theorem to Banach algebras and operators between Banach…

This paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in $\C^2$. We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the…

We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…

The dynamical degree $\lambda(f)$ of a birational transformation $f$ measures the exponential growth rate of the degree of the formulae that define the $n$-th iterate of $f$. We study the set of all dynamical degrees of all birational…

We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…

We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For normal operators on Hilbert space and polynomial or holomorphic…