Abstract

After exploiting the role of Lie symmetries in understanding the time properties of planar centers, recent works have focused on the implications of Lie symmetries on some features of limit cycles. In this talk, we will give an overview of such results, with special attention to the use of the symmetries both for the study of the stability of limit cycles and for controlling the isochrones of the limit cycle. In the first part, we will relate the Lie brackets with the existence of Dulac functions, giving a new way to obtain candidates of Dulac functions. In the second part, we will examine methods to obtain the isochrones of limit cycles, which cover the range from purely analytic to purely numeric.We will end the talk with some open questions, some of them with biological interest