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Title: The topology of integrable systems with incomplete fields

Abstract

Liouville's theorem holds for Hamiltonian systems with complete Hamiltonian fields which possess a complete involutive system of first integrals; such systems are called Liouville-integrable. In this paper integrable systems with incomplete Hamiltonian fields are investigated. It is shown that Liouville's theorem remains valid in the case of a single incomplete field, while if the number of incomplete fields is greater, a certain analogue of the theorem holds. An integrable system on the algebra sl(3) is taken as an example. Bibliography: 11 titles.

Authors:
 [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22364892
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 205; Journal Issue: 9; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; HAMILTONIANS; INTEGRAL CALCULUS; INTEGRALS; LIOUVILLE THEOREM; MATHEMATICAL SOLUTIONS; SL GROUPS; TOPOLOGY

Citation Formats

Aleshkin, K R. The topology of integrable systems with incomplete fields. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N09ABEH004417.
Aleshkin, K R. The topology of integrable systems with incomplete fields. United States. https://doi.org/10.1070/SM2014V205N09ABEH004417
Aleshkin, K R. 2014. "The topology of integrable systems with incomplete fields". United States. https://doi.org/10.1070/SM2014V205N09ABEH004417.
@article{osti_22364892,
title = {The topology of integrable systems with incomplete fields},
author = {Aleshkin, K R},
abstractNote = {Liouville's theorem holds for Hamiltonian systems with complete Hamiltonian fields which possess a complete involutive system of first integrals; such systems are called Liouville-integrable. In this paper integrable systems with incomplete Hamiltonian fields are investigated. It is shown that Liouville's theorem remains valid in the case of a single incomplete field, while if the number of incomplete fields is greater, a certain analogue of the theorem holds. An integrable system on the algebra sl(3) is taken as an example. Bibliography: 11 titles.},
doi = {10.1070/SM2014V205N09ABEH004417},
url = {https://www.osti.gov/biblio/22364892}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 9,
volume = 205,
place = {United States},
year = {Tue Sep 30 00:00:00 EDT 2014},
month = {Tue Sep 30 00:00:00 EDT 2014}
}