Limit cycles for 3-monomial differential equations

作者：Gasull, Armengol; Li, Chengzhi; Torregrosa, Joan^*

来源：Journal of Mathematical Analysis and Applications, 2015, 428(2): 735-749.

DOI：10.1016/j.jmaa.2015.03.039

• Limit cycles
• Homogeneous nonlinearities
• Abelian integrals
• Bifurcations
• Z(q)-equivariant symmetry

lAre study planar polynomial differential equations that in complex coordinates write as (z) over dot = Az + Bz(z)(k)(-l) + Cz(m) (z) over tilde (n). We prove that for each p is an element of N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case (z) over dot = Az + B (z) over bar + Cz(m)(z) over bar (n), which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.

• 出版日期2015-8-15
• 单位北京大学