Real forms of the complex Neumann system : a method for finding real roots of polynomial Us([lambda])

Novak, Tina (author), Žerovnik, Janez (author)

The topology of Arnold-Liouville level sets of the real forms of the complex generic Neumann system depends indirectly on the positions of the roots of the special polynomial Us ([lambda]). For certain polynomials, the existence and positions of the real roots, according to the suitable parameters of the system, is not obvious. In the paper, a method for checking the existence and positions of the real roots of the polynomials Us ([lambda]) is given. The method and algorithm are based on searching of a positive solution of a system of linear equations. In case [eta]=2 , we provide a complete solution to the problem of existence of real roots for all special polynomials and determine the topology of the Arnold-Liouville level sets.

• Language: English
• Keywords: roots of a polynomial, complex Neumann system, Arnold-Liouville level sets, positive solution, system of linear equations
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2021
• Number of pages: 13 str.
• Numbering: Vol. 390, art. 113362
• PID: 20.500.12556/RUL-134490
• UDC: 512.6(045)
• ISSN on article: 0377-0427
• DOI: 10.1016/j.cam.2020.113362
• COBISS.SI-ID: 45201667
• Publication date in RUL: 18.01.2022

Record is a part of a journal

• Title: Journal of computational and applied mathematics
• Shortened title: J. comput. appl. math.
• Publisher: Elsevier
• ISSN: 0377-0427
• COBISS.SI-ID: 27496960

Secondary language

• Language: Slovenian
• Keywords: ničle polinoma, kompleksen Neumannov sistem, Arnold-Liouvilleove nivojske množice, pozitivna rešitev, sistem linearnih enačb

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0248
• Name: Inovativni izdelovalni sistemi in procesi

• Funder: ARRS - Slovenian Research Agency
• Project number: J2-2512
• Name: Stohastični modeli za logistiko proizvodnih procesov