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13 p, 712.8 KB Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension / Barreira, Luis (Instituto Superior Técnico (Portugal). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We study the limit cycles which can bifurcate from a zero--Hopf singularity of a C^m 1 differential system in \R^n, i. e. from a singularity with eigenvalues b i and n-2 zeros for n 3. If this singularity is at the origin of coordinates and the Taylor expansion of the differential system at the origin without taking into account the linear terms starts with terms of order m, from the origin it can bifurcate s limit cycles with s \ 0,1, 2^n-3\ if m=2 (see LZ), with s \ 0,1, 3^n-2\ if m=3, with s 6^n-2 if m=4, and with s 4 5^n-2 if m=5. [...]
2018 - 10.1007/s11071-018-4115-3
Nonlinear dynamics, Vol. 92, issue 3 (May 2018) , p. 1159-1166  

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