Related papers: Ergodic solenoids and generalized currents
A rigid current on a compact complex manifold is a closed positive current whose cohomology class contains only one closed positive current. Rigid currents occur in complex dynamics, algebraic and differential geometry. The goals of the…
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe…
We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. These include the possibility of a globally smooth phase convention for electric fields for all points on the Poincar\'{e}…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
Let $\Sigma$ be a closed orientable hyperbolic surface. We introduce the notion of a \textit{geodesic current with corners} on $\Sigma$, which behaves like a geodesic current away from certain singularities (the "corners"). We topologize…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
In the first part of our generalized ergodic theory we introduced Cantor-systems, when we managed to prove the generalized ergodic theorem 3.3. The first component of a Cantor-system is a group of the flow and its second component is a set…
We review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel…
This text is the extended version of a talk given at the conference Geometry, Topology, QFT and Cosmology hold from May 28 to May 30, 2008 at the Observatoire de Paris. We explore the notion of solder (or soldering form) in differential…
We show that every multilinear map between Euclidean spaces induces a unique, continuous, Minkowski multilinear map of the corresponding real cones of zonoids. Applied to the wedge product of the exterior algebra of a Euclidean space, this…
In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in…
In this paper, we present a proof of Schauder estimate on Euclidean space and use it to generalize Donaldson's Schauder estimate on space with conical singularities in the following two directions. The first is that we allow the total cone…
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
The aim of this short paper is threefold. First, we develop an implicit generalization of a constitutive relation introduced by Korteweg [10] that can describe the phenomenon of capillarity. Second, using a sub-class of the constitutive…
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic measures with finite moments. The main technical tool is duality combined with successful coupling.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called…
New phenomenological approach for the description of elementary collective excitations is proposed. The crystal is considered to be an anisotropic space-time vacuum with a prescribed metric tensor in which the information on electromagnetic…
We present a canonical quantization of electromagnetic modes in cylindrical waveguides, extending a gauge-based formalism previously developed for Cartesian geometries [1]. By introducing the two field quadratures $X,Y$ of TEM (transverse…
We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test-bodies with horizons and…