Dulac Functions of Planar Vector Fields

作者：Gine Jaume^*

来源：Qualitative Theory of Dynamical Systems, 2014, 13(1): 121-128.

DOI：10.1007/s12346-014-0108-x

• Analytic differential systems
• Dulac functions
• Limit cycles
• Planar analytic vector fields

In this work we give sufficient conditions for the existence of a Dulac function for an arbitrary differential system. This Dulac function allows to discard the existence of limit cycles in its domain of definition if this domain is a simply connected region. If the domain of definition is -multiple connected then the Dulac function can estimate the number of limit cycles inside the domain.

• 出版日期2014-4