Related papers: Pull-back of currents by holomorphic maps
In this paper we define currents relative to a free factor system. We prove that a fully irreducible outer automorphism relative to a free factor system acts with uniform north-south dynamics on a subspace of the space of projective…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
In this paper we will develop a general approach which shows that generalized "critical relations" of families of locally defined holomorphic maps on the complex plane unfold transversally. The main idea is to define a transfer operator,…
We describe some examples of classical and explicit h-transforms as particular cases of a general mechanism, which is related to the existence of symmetric diffusion operators having orthogonal polynomials as spectral decomposition.
This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
We introduce a notion of super-potential (canonical function) associated to positive closed (p,p)-currents on compact Kaehler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of…
The multipolar decomposition of current distributions is used in many branches of physics. Here, we obtain new exact expressions for the dipolar moments of a localized electric current distribution. The typical integrals for the dipole…
In this paper, we extend the ideas of certain notions that one studies in thermodynamic formalism of maps to the context when the dynamics in the phase space evolves by complex holomorphic correspondences. Towards that end, we define the…
The reduction of the three-dimensional classical electromagnetism is performed in a twofold way. In the first case the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing…
We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…
For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the…
We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive…
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
We introduce the formalism of positive super currents on \mathbb{R}^{n}, in strong analogy with the theory of positive currents in \mathbb{C}^{n}. We consider intersection of currents and Lelong numbers, and as an application we show that…
On Riemannian signature conformal 4-manifolds we give a conformally invariant extension of the Maxwell operator on 1-forms. We show the extension is in an appropriate sense injectively elliptic, and recovers the invariant gauge operator of…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…