Related papers: Some remarks about solenoids, 2
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
Some aspects of the multidimensional soliton geometry are considered.
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…
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.
In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open…
We develop the dimension theory for a class of linear solenoids, which have a "fractal" attractor. We will find the dimension of the attractor, proof formulas for the dimension of ergodic measures on this attractor and discuss the question…
Some aspects of multidimensional soliton geometry are considered.
A basic class of constructions is considered, in connection with bilipschitz mappings in particular.
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
We study the fractal dimension of a class of solenoidal attractors in dimensions greater or equal than 3, proving that if the contraction is sufficiently strong, the expansion is close to conformal and the attractor satisfy a geometrical…
Here we look at some related constructions of solenoids, and mappings associated to them.
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own…
Zonoids whose polars are zonoids cannot have proper faces of dimension other than $n-1$ or zero ($n\geq 3$). However, there exist non smooth zonoids whose polars are zonoids. Examples in $R^3$ and $R^4$ are given.
Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are…
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…
Some elementary considerations are presented concerning Catenoids and their stability, separable minimal hypersurfaces, minimal surfaces obtainable by rotating shapes, determinantal varieties, minimal tori in S3, the minimality in Rnk of…
In the first part, we revisit the theory of Drinfeld modular curves and $\pi$-adic Drinfeld modular forms for GL(2) from the perfectoid point of view. In the second part, we review open problems for families of Drinfeld modular forms for…
This article provides a complete characterization of the conformal classes of product tori and standard flat tori in complex dimension 1 (real dimension 2). Utilizing basic differential geometry methods, our approach contrasts with…