Addendum in `Silva, Vinícius B. et al., 2018, A new application of the normal form description to a N-dimensional dynamical systems attending the conditions of a Hopf bifurcation, Journal of Vibration Testing and System Dynamics, 2(3), 249-256'

Vinícius B. Silva1; João P. Vieira2; Edson D. Leonel1; 3

Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Addendum in `Silva, Vinícius B. et al., 2018, A new application of the normal form description to a N-dimensional dynamical systems attending the conditions of a Hopf bifurcation, Journal of Vibration Testing and System Dynamics, 2(3), 249-256'

Journal of Vcibration Testing and System Dynamics 3(3) (2019) 369--371 | DOI:10.5890/JVTSD.2019.09.008

Vinícius B. Silva$^{1}$, João P. Vieira$^{2}$, Edson D. Leonel$^{1}$,$^{3}$

$^{1}$ Departamento de Física, UNESP - Universidade Estadual Paulista, Av. 24A, 1515 - Bela Vista, 13506-900, Rio Claro, SP, Brazil

$^{2}$ Departamento de Matemática, UNESP - Universidade Estadual Paulista, Av. 24A, 1515 - Bela Vista, 13506-900, Rio Claro, SP, Brazil

$^{3}$ Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

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Abstract

In the underlying work, a general theorem for the derivation of the normal form of N-dimensional systems reduced to its center manifold is proposed and proved. In the present addendum, some observations regarding the conditions of the theorem are added. The corrections and the additions not only don’t aﬀect the value of the best part of the published article but also enhance the value of the original manuscript.

References

[1] Hopf, E., Morawetz, S., Serrin, J. (2002), Selected Works of Eberhard Hopf:With Commentaries, American Mathematical Society: Providence, Rhode Island.