Related papers: Ergodic solenoids and generalized currents
Previous work of the author has developed coordinates on bundles over the classical Teichmueller spaces of punctured surfaces and on the space of cosets of the Moebius group in the group of orientation-preserving homeomorphisms of the…
The space of non-singular flows on any given solenoid is shown to contain a generic subset consisting of flows that are not almost periodic. Whether this result carries over to Hamiltonian flows remains an open question.
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
A self-consistent general relativistic configuration describing a finite cross-section magnetic flux tube is constructed. The cosmic solenoid is modeled by an elastic superconductive surface which separates the Melvin core from the…
A G-solenoid is a laminated space whose leaves are copies of a single Lie group G, and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as dynamical system. Free Z^d-actions on the Cantor set as…
Let $S$ be a compact, connected, oriented surface, possibly with boundary, of negative Euler characteristic. In this article we extend Lindenstrauss-Mirzakhani's and Hamenst\"adt's classification of locally finite mapping class group…
Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…
The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…
A new generalisation of the notion of space, called "vectoid", is suggested in this work. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated…
Our conception of a generalized ergodic theory shall exceed the generality of general topology: In this first part of the generalized ergodic theory we investigate the logical constitution of the conception of attractors. We prepare a…
Inspired by work of Borzellino and Brunsden, we generalize the notion of a submanifold identifying a natural and sufficiently general condition which guarantees that a subset of an (effective) orbifold carries itself a canonical induced…
The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than it is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely…
The generalization of electromagnetic and gravitational hopfions is performed in terms of a complex scalar field. New definition of topological charge for linearized gravity is given. Quasi-local (super-)energy densities are compared for…
A point is called generic for a flow preserving an infinite ergodic invariant Radon measure, if its orbit satisfies the conclusion of the ratio ergodic theorem for every pair of continuous functions with compact support and non-zero…
We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to…
The Bohr-Fourier series development on one dimensional solenoids is analyzed by using invariant functions and extending Bohr's theory through the study of transversal variation
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…