Limit cycles of linear vector fields on manifolds

作者：Llibre, Jaume^*; Zhang, Xiang

来源：Nonlinearity, 2016, 29(10): 3120-3131.

DOI：10.1088/0951-7715/29/10/3120

• limit cycle
• periodic orbit
• centre
• isochronous centre
• averaging method

It is well known that linear vector fields on the manifold R-n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C-1 connected manifold.

• 出版日期2016-10
• 单位上海交通大学