# 1. Classical and Modern Topology 2. Topological Phenomena in Real World Physics

@article{Novikov20101CA, title={1. Classical and Modern Topology 2. Topological Phenomena in Real World Physics}, author={Sergey P. Novikov}, journal={arXiv: Mathematical Physics}, year={2010}, pages={406-424} }

According to the Ancient Greeks, the famous real and mythical founders of Mathematics and Natural Philosophy, such as Pythagoras, Aristotle and others, in fact, borrowed them from the Egyptian and Middle Eastern civilizations. However, what had been told before in the hidden mysteries Greek scientists transformed into written information acceptable to everybody. Immediately after that the development of science in the modern sense started and had already reached a very high level 2000 years ago…

## 9 Citations

A Conjecture on the Hausdorff Dimension of Attractors of Real Self-Projective Iterated Function Systems

- MathematicsExp. Math.
- 2015

This work introduces a certain family of semigroups, and suggests that for n ≥ 3, (n − 1)sA/n is a lower bound for the Hausdorff dimension of RA.

Quasiperiodic functions on the plane and electron transport phenomena

- Mathematics, Physics
- 2018

While quasiperiodic functions in one variable appeared in applications since Eighteen hundreds, for example in connection with the trajectories of mechanical systems with 2n degress of freedom having…

Localization properties of squeezed quantum states in nanoscale space domains

- Physics
- 2013

We construct families of squeezed quantum states on an interval (depending on boundary conditions, we interpret the interval as a circle or as the infinite square potential well) and obtain estimates…

BETWEEN LOWER AND HIGHER DIMENSIONS ( in the work of Terry Lawson )

- Education

There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed…

TANGENTIAL THICKNESS OF HOMOTOPY LENS SPACES

- Mathematics

Given two nonhomeomorphic topological spaces X and Y , it is often interesting or important to specify necessary or sufficient conditions for X ×R and Y ×R to be homeomorphic, where as usual R…

Exponential growth of norms in semigroups of linear automorphisms and Hausdor dimension of self-projective IFS.

- Mathematics
- 2012

Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of…

Quasiperiodic Dynamics and Magnetoresistance in Normal Metals

- Mathematics, PhysicsActa Applicandae Mathematicae
- 2019

In this article we give a brief survey on the physics and mathematics of the phenomenon of conductivity in metals under a strong magnetic field.

Squeezed quantum states on an interval and uncertainty relations for nanoscale systems

- Physics
- 2009

We construct families of squeezed quantum states on an interval and analyze their asymptotic behavior. We study the localization properties of a kind of such states constructed on the basis of the…

PIECEWISE LINEAR STRUCTURES ON TOPOLOGICAL MANIFOLDS

- Mathematics
- 2015

This is a survey paper where we expose the Kirby--Siebenmann results on classification of PL structures on topological manifolds and, in particular, the homotopy equivalence TOP/PL=K(Z/2.3) and the…

## References

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For any Phase space, i.e. a manifold M with the Poisson structure, we have a scew-symmetric Poisson Tensor h ij with 2 upper indices in any local coordinates (x i ), such that the Poisson Bracket…

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It is shown that the investigation of the conductivity in a single crystal of a normal metal with a complicated Fermi surface in strong magnetic fields B can reveal integral topological…

The geometry of stability regions in Novikov's problem on the semiclassical motion of an electron

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Contents § 1. Introduction1.1. Statement of results § 2. The algebraic density of closed trajectories and the Euler characteristic2.1. Types of trajectories. Degree of irrationality2.2. Stability of…

Existence and measure of ergodic leaves in Novikov's problem on the semiclassical motion of an electron

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CONTENTS Introduction § 1. The Hamiltonian formalism. Simplest examples. Systems of Kirchhoff type. Factorization of the Hamiltonian formalism for the B-phase of 3He § 2. The Hamiltonian formalism of…

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Geometry of stability zones in the Novikov's problem on the semiclassical motion of an electron, Russian Math Surveys

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