Related papers: Pull-back of currents by meromorphic maps

Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…

Let $X$ be a compact K\"ahler manifold of dimension 3 and let $f:X\rightarrow X$ be a pseudo-automorphism. Under the mild condition that $\lambda_1(f)^2>\lambda_2(f)$, we prove the existence of invariant positive closed $(1,1)$ and $(2,2)$…

Persistent currents in disordered mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalization methods in the one-dimensional (1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D) systems.…

This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS94-4-1] to construct maps $\Phi:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of…

The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…

We consider the space $\mathcal{D}'^r_L(M;E)$ of distributional sections of the smooth complex vector bundle $E\rightarrow M$ whose Sobolev wave front set of order $r\in\mathbb{R}$ lies in the closed conic subset $L$ of $T^*M\backslash0$.…

Under some mild assumptions, an orientation-preserving branched covering map of marked $2$-spheres induces a pullback map between the corresponding Teichm\"uller spaces. By analyzing the associated pushforward operator acting on integrable…

Let $i\colon X \to Y$ be pure-dimensional reduced subvariety of a smooth manifold $Y$. We prove that the direct image of pseudomeromorphic currents on $X$ are pseudomeromorphic on $Y$. We also prove a partial converse: if $i_*\tau$ is…

A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By Hahn-Banach theorem, a positive strong submeasure is…

Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued…

Let S be a Pfaff system of dimension 1, on a compact complex manifold M. We prove that there is a positive ddbar-closed current T of mass 1 directed by the Pfaff system S. There is no integrability assumption. We also show that local…

In this article, we introduce fundamental notions and results about pullback formalisms, building on work of Drew-Gallauer. Our main application is producing a pullback formalism $\mathbf{SH}^{\mathrm{hol}}$ that encodes a version of…

We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient conditions for existence of Green currents in…

We use Almgren's framework of multi-valued maps to construct a multi-valued inverse $F:f(\Omega)\to \mathcal A_d(\mathbb R^n)$ of a quasiregular map $f:\Omega\to \mathbb R^n$ of finite degree $d$. We then develop a pull-back theory of…

We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of…

We show that any dynamics on any discrete planar sequence $S$ can be realized by the postsingular dynamics of some transcendental meromorphic function, provided we allow for small perturbations of $S$. This work was influenced by an…

We construct the Green current for a random iteration of "horizontal-like" mappings in two complex dimensions. This is applied to the study of a polynomial map $f:\mathbb{C}^2\to\mathbb{C}^2$ with the following properties: 1. infinity is…

The existence of a finite global attractor for polynomial curve system has been known since the work of Belk et al. [4]. However, except in the hyperbolic case, the rate at which the pullback of a curve under a polynomial converges to the…

We investigate the intersection of positive closed currents in a general setting, employing tangent currents alongside King's residue formula. Our main result establishes a natural condition for the intersection--namely, the Dinh-Sibony…

We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing the notion of a {\it strong Lyapunov function} for an…