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Applied Physics and Mathematics Annotation << Back
NONSMOOTH MAPPINGS. STATIONARY MODELS AND PROBLEMS
OF NONSMOOTH DYNAMICS AND ELECTRODYNAMICS. PART 2 |
A.V. KUKUSHKIN
I propose an adequate terminology for operations with multivalued
algebraic functions on the complex plane (not on
a Riemann surface) with deleted branch points, where the
derivative of the function has a pole. For the complex plane
with this property, I suggest the name «Riemann plane». It
is shown that the special properties of the «Riemann plane»
permit to create the theory of non-smooth coordinate
transformations on the real plane based on conformal
mappings. In this way, the fundamentals of constructing
curvilinear coordinate systems with non-smooth coordinate
lines are being formulated. Such systems are being shown
to be able to mirror image unknown properties of known
physical phenomena from dynamics and electrodynamics. In
particular, for non-smooth problems in electrodynamics there
is an eff ect that can be described as a local violation of the
solenoidal nature of the magnetic fi eld.
Key words: non-smooth mappings, catastrophe theory, problems
of non-smooth dynamics and electrodynamics, coordinate
lines with points of nonsmoothness, «Riemann plane» (not on a
surface), singular saddle point fi eld, a local violation of the solenoidal
nature of the magnetic fi eld
Contacts: E-mail: avkuku @gmail.com
Pp. 41-56. |
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