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Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems

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  • Algaba, A.
  • García, C.
  • Reyes, M.

Abstract

We characterize the nilpotent systems whose lowest degree quasi-homogeneous term is (y,σxn)T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the systems with formal inverse integrating factor are formally orbital equivalent to (x˙,y˙)T=(y,xn)T. In the case n odd, we give a formal normal form that characterizes them. As a consequence, we give the link among the existence of formal inverse integrating factor, center problem and integrability of the considered systems.

Suggested Citation

  • Algaba, A. & García, C. & Reyes, M., 2012. "Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 869-878.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:869-878
    DOI: 10.1016/j.chaos.2012.02.016
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    Cited by:

    1. Algaba, A. & Fuentes, N. & Gamero, E. & García, C., 2021. "On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Algaba, A. & Fuentes, N. & Gamero, E. & García, C., 2020. "Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh–Nagumo system," Applied Mathematics and Computation, Elsevier, vol. 369(C).

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