Preview

Civil Aviation High Technologies

Advanced search

ON THE PROBLEM OF TORE DIFFEOMORPHISM EXTENSION AND ITS APPLICATIONS

Abstract

The construction of the extensions of a 2-torus diffeomorphism up to volume preserving diffeomorphism of solid tori is proposed. The construction is illustrated on the example of extension of diffeomorphism of action on the torus. These extensions are used for the construction of kinematic dynamo examples onto solid torus. For the case of n -sphere a generation of results obtained before is proposed.

About the Author

A. M. Lukatsky
институт энергетических исследований (ИНЭИ) РАН
Russian Federation


References

1. Задачи Арнольда. - М.: ФАЗИС, 2000. - С. 71.

2. Лукацкий А.М. О задаче продролжения диффеоморфизмов // Анализ и особенности (Арнольд-75): тезисы междунар. конф. - М.: МИ РАН, 2012. - С. 77-78.

3. Lukatsky A.M. A Construction of Diffeomorphism Extension and its Applications // Научный Вестник МГТУ ГА. - 2014. - № 204.

4. Виленкин Н.Я. Специальные функции и теория представлений групп. - М.: Наука, 1965.

5. Жук В.В., Натансон Г.И. Тригонометрические ряды Фурье и элементы теории аппроксимации. - Ленинград: Изд-во Ленинградского ун-та, 1983. - С. 188.

6. Thurston W. Folliations and Groups of Diffeomorphisms. Bul. A.M.S., 1975, Vol. 80, p.p. 304-307.

7. Hermam M.R. Sur le groupe des diffeomorphismes R-analitiques du tore. Diff. Top. and Geom. (Proc. Colloq. Dijon, 1974) (Lect. Notes. Math., 484) Springer, Berlin, 1975, p.p. 36-42.

8. Арнольд В.И., Хесин Б.А. Топологические методы в гидродинамике. - М.: МЦНМО, 2007.


Review

For citations:


Lukatsky A.M. ON THE PROBLEM OF TORE DIFFEOMORPHISM EXTENSION AND ITS APPLICATIONS. Civil Aviation High Technologies. 2014;(207):133-137. (In Russ.)

Views: 331


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2079-0619 (Print)
ISSN 2542-0119 (Online)