Local Integrability and Linearizability of a $$(1:-1:-1)$$(1:-1:-1) Resonant Quadratic System
Local Integrability and Linearizability of a $$(1:-1:-1)$$(1:-1:-1) Resonant Quadratic System
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DOI：
10.1007/s10884-015-9486-2
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发表时间：
2017-06
影响因子：
1.3
通讯作者：
M. Dukarić;Regilene D. S. Oliveira;V. Romanovski
中科院分区：
文献类型：
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作者：
M. Dukarić;Regilene D. S. Oliveira;V. Romanovski
In this paper we study the local integrability and linearizability of quadratic three dimensional systems of the form First, we obtain necessary and sufficient conditions for the complete integrability and linearizability of this system. Then, we discuss the problem of existence of one first integral of the form ψ^(1)(x, y, z)= xy+ O (| x, y, z|^ 3) ψ (1)(x, y, z)= xy+ O (| x, y, z| 3). Computation of resonant focus quantities and the decomposition of the variety of the ideal that they generate in the ring of polynomials of parameters a_ ij, b_ ij, c_ ij aij, bij, cij of the system were used to obtain necessary conditions of integrability and linearizability. The theory of Darboux integrability and some other methods are used to show the sufficiency. In the investigation of the conditions for the existence of one first integral the decomposition of the variety mentioned above was performed using modular computations, its consequences are discussed.
