Linearizability conditions for a cubic system

Linearizability of homogeneous quartic polynomial systems with 1:−2 resonance

“…For p = 1 and q = 2, the quadratic system is studied in [2]. More studies can be found in, e.g., [1,4,[10][11][12][13][14]. For general p and q, even for quadratic systems, this problem is still open.…”

Integrability of Lotka–Volterra Planar Complex Cubic Systems

“…More specifically they considered the systems where one of the coefficients a 10 , a 01 and a −12 is different from zero and one of the coefficients a 20 , a 11 , a 02 and a −13 is equal to zero. In [Dolinićanin et al, 2007] the linearizability of complex cubic system of the forṁ…”

Centers and isochronicity of some polynomial differential systems

“…In such case if we can find or at least prove the existence of a first integral of system (1.24) then it can be possible to construct linearizing transformations, as stated in the following two theorems. For the proofs see [103] and [38], respectively. Theorem 1.4.5.…”

“…In the investigation of conditions for the linearizability of a weakly persistent center of system (5.3) we obtain the following result. Note that the Lotka-Volterra systems considered in [27], [38] and [102] are all subcases of (5.3). We compute the first six pairs of linearizability quantities, i 1 , j 1 , ..., i 6 , j 6 of system (5.19).…”

“…(5.3) and (5.19) arė x = ix + x(a 20 x + a 12 y 2 ),ẏ = −iy + y(b 02 y + b 03 y 2 ), (5.30) andẋ = ix + λ x(a 20 x + a 12 y 2 ),ẏ = −iy + λ y(b 02 y + b 03 y 2 ), (5.31)respectively. System (5.30) is considered in[38, Theorem 2, case 3], where the corresponding linearizable change of coordinates is obtained. So, by Lemma 5.2.3 system (5.31) is linearizable.…”