The solution of some  persistent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
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</mml:math> resonant center problems

Žulj, Maja; Ferčec, Brigita; Mencinger, Matej

doi:10.14232/ejqtde.2018.1.99

Cited by 4 publications

(9 citation statements)

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“…linearizes the second equation of the system. The integrability of the above quadratic system has been proven in [22]. Using Theorem 3, we can also linearize the first equation; thus, system (20) is linearizable.…”

Section: The Linearizability Conditionsmentioning

confidence: 90%

“…which is a formal first integral of ( 22) of the required form, and due to ([1], Corollary 3.2.6), it is also the analytic first integral of (22). Finally, we can form the linearizing transformation of the first equation of system (22), as stated in Theorem 3. Case (5) We find three algebraic partial integrals:…”

Section: The Linearizability Conditionsmentioning

confidence: 94%

“…. [22]. According to Theorem 2, the second equation of system is linearized by transformation y 1 = Ψ Case (10) The linearizability of the corresponding system is proven in a similar way as in Case ( 4), using the method based on blow-up.…”

Section: The Linearizability Conditionsmentioning

confidence: 99%

“…. that linearizes the second equation of system (22). In system (22), we perform the blow-up transformation (x, y) → (z, y) = ( x y , y) and attain the following systemż…”

Section: The Linearizability Conditionsmentioning

confidence: 99%

“…where polynomials P i (z) are defined by (27). Thus, the transformation y 1 (x, y), which linearizes the second equation of system (22), is…”

Section: The Linearizability Conditionsmentioning

confidence: 99%

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Linearizability of 2:−3 Resonant Systems with Quadratic Nonlinearities

2021

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In this paper, the linearizability of a 2:−3 resonant system with quadratic nonlinearities is studied. We provide a list of the conditions for this family of systems having a linearizable center. The conditions for linearizablity are obtained by computing the ideal generated by the linearizability quantities and its decomposition into associate primes. To successfully perform the calculations, we use an approach based on modular computations. The sufficiency of the obtained conditions is proven by several methods, mainly by the method of Darboux linearization.

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Section: The Linearizability Conditionsmentioning

confidence: 90%

Section: The Linearizability Conditionsmentioning

confidence: 94%

Section: The Linearizability Conditionsmentioning

confidence: 99%

“…. that linearizes the second equation of system (22). In system (22), we perform the blow-up transformation (x, y) → (z, y) = ( x y , y) and attain the following systemż…”

Section: The Linearizability Conditionsmentioning

confidence: 99%

“…where polynomials P i (z) are defined by (27). Thus, the transformation y 1 (x, y), which linearizes the second equation of system (22), is…”

Section: The Linearizability Conditionsmentioning

confidence: 99%

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