On universal relations in Gauge theory

In this paper we study the algebraic topology of gauge group, and as a corollary we deduce some universal relations among Donaldson polynomials of smooth 4-manifolds.

     

Gauge invariance of the dimension-two condensate in the Yang-Mills theory

We demonstrate the gauge independence of the dimension-two vacuum condensate in the Yang-Mills theory using a noncommutative theory technique.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 3–8, April, 2005.     

Gauge group and gauge transformation in the continual theory of defects

A representation of the algebra (3)=t(3) S0(3, ) by differential Schaefer's operators is proposed, and an external algebra of (3)-valued differential forms is constructed. The requirement of local gauge invariance is formulated in the model of the (3)-valued field, which enables a group of gauge transformations of the continual theory of defects to be obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 173–184, 1991.I wish to thank V. N. Popov for his interest.     

A uniqueness theorem in the dynamical theory of piezoelectricity

The solution to the linearized equations of dynamical linear piezoelectricity is shown to be unique without requiring definiteness conditions in the elastic coefficients. Only continuity of the normal component of the electric displacement field across the boundary between the elastic body and free space is required. The proof employs a logarithmic convexity argument.     

Deformation theory of quantizable dynamical systems

Deformations of families of quantizable dynamical systems are introduced and the local extension problem for quantizable dynamical systems is solved. This research was supported in part by NSF GP-13375 and NSF GP-20856. Entrata in Redazione il 2 dicembre 1970.     

Ergodic theory of differentiable dynamical systems

Iff is a C^{1 + ɛ} diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost everywhere with respect to everyf-invariant probability measure on M. These stable manifolds are smooth but do not in general constitute a continuous family. The proof of this stable manifold theorem (and similar results) is through the study of random matrix products (multiplicative ergodic theorem) and perturbation of such products. Dedicated to the memory of Rufus Bowen     

Qualitative theory of p-adic dynamical systems

We consider a class of dynamical systems over the p-adic number field: hierarchical dynamical systems. We prove a strong variant of the Poincaré theorem on the number of returns for such systems and show that hierarchical systems do not admit mixing. We describe hierarchical dynamical systems over the projective line and present an example of a nonhierarchical p-adic system that admits mixing: the p-adic baker’s transformation.     

Number theoretical peculiarities in the dimension theory of dynamical systems

We show that dimensional theoretical properties of dynamical systems can considerably change because of number theoretical peculiarities of some parameter values. Supported by “DFG-Schwerpunktprogramm — Dynamik: Analysis, effiziente Simulation und Ergodentheorie”. We refer to the book of Falconer [6] for an introduction to dimension theory and recommend the book of Pesin [17] for the dimension theory of dynamical systems.