Related papers: Some remarks about solenoids
A class of solenoids is considered, including some aspects in n (topological) dimensions, where one basically gets some fractal versions of tori.
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
A basic class of constructions is considered, in connection with bilipschitz mappings in particular.
We comment on a recent paper regarding the derivation of the magnetic field components of a solenoid in analytical form by proposing a different and simpler method
We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented…
An alternative elementary argument for the magnetic field outside a solenoid is described.
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
Some aspects of the multidimensional soliton geometry are considered.
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse…
Solenoids are inverse limit spaces over regular covering maps of closed manifolds. M.C. McCord has shown that solenoids are topologically homogeneous and that they are principal bundles with a profinite structure group. We show that if a…
We classify toroidal solenoids defined by non-singular $n\times n$-matrices $A$ with integer coefficients by studying associated first \^Cech cohomology groups. In a previous work, we classified the groups in the case $n=2$ using…
We discuss a concept of loopoid as a non-associative generalization of (Brandt) groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as…
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
We define the bounded coarse structure attached to a family of pseudometrics and give some counterexamples to conjectures that arise naturally.
Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections…
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.
We define a new family of valuations on polyhedral cones valued in the space of bounded polyhedra.
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…
Solenoids induced by split sequences are introduced, as the inverse limit object of a sequence of fold maps. The topology of a solenoid is explored, and it is established that solenoids have naturally arising singular foliated structures.…