The comitants of Lyapunov system with respect to the rotation group and applications

Pricop Victor

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PRICOP, Victor. The comitants of Lyapunov system with respect to the rotation group and applications. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, p. 41. ISBN 978-9975-76-247-2.

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Conference on Applied and Industrial Mathematics
Ediţia a 26-a, 2018

Conferința "Conference on Applied and Industrial Mathematics"
Iași, România, Romania, 20-22 septembrie 2018

The comitants of Lyapunov system with respect to the rotation group and applications

Pag. 41-41

Pricop Victor¹²

¹ "Ion Creangă" State Pedagogical University from Chisinau,
² Vladimir Andrunachievici Institute of Mathematics and Computer Science

Disponibil în IBN: 31 mai 2022

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Let us consider the Lyapunov system sL(1;m1; :::;m`) x_ = y + X` i=1 Pmi (x; y); y_ = -x + X` i=1 Qmi (x; y); (1) where Pmi and Qmi are homogeneous polynomials of degree mi with respect to phase variables x and y. The set f1;m1; :::;m`g consists of a nite number of distinct natural numbers. With A is denoted the set of coecients of Pmi and Qmi . We investigate the action of the rotation group SO(2;R) on the system (1). Following [1] analogically were de ned the comitants of di erential systems with respect to the rotation group. The Lie operator of the representation of the group SO(2;R) in the space EN(x; y;A) of the system (1) was de ned [2]. Using this Lie operator was determined the criterion when a polynomial is a comitant of Lyapunov system with respect to the rotation group. Theorem 1. The number of functionally independent focus quantities in the center and focus problem for the Lyapunov system sL(1;m1; :::;m`) does not exceed the number

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