Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 473-484
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In this paper we study the local bifurcation of critical periods of periodic orbits in the neighborhood of a nondegenerate centre of a vector field with a homogeneous nonlinearity of the third degree. We show that at most three local critical periods bifurcate from a weak linear centre of finite order or from the linear isochrone and at most two local critical periods from the nonlinear isochrone. Moreover, in both cases, there are perturbations with the maximum number of critical periods.
Rousseau, C. Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree. Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 473-484. doi: 10.4153/CMB-1993-063-7
@article{10_4153_CMB_1993_063_7,
author = {Rousseau, C.},
title = {Local {Bifurcation} of {Critical} {Periods} in {Vector} {Fields} {With} {Homogeneous} {Nonlinearities} of the {Third} {Degree}},
journal = {Canadian mathematical bulletin},
pages = {473--484},
year = {1993},
volume = {36},
number = {4},
doi = {10.4153/CMB-1993-063-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-063-7/}
}
TY - JOUR AU - Rousseau, C. TI - Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree JO - Canadian mathematical bulletin PY - 1993 SP - 473 EP - 484 VL - 36 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-063-7/ DO - 10.4153/CMB-1993-063-7 ID - 10_4153_CMB_1993_063_7 ER -
%0 Journal Article %A Rousseau, C. %T Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree %J Canadian mathematical bulletin %D 1993 %P 473-484 %V 36 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-063-7/ %R 10.4153/CMB-1993-063-7 %F 10_4153_CMB_1993_063_7
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