An example of rapid evolution of complex limit cycles

Details An example of rapid evolution of complex limit cycles An example of rapid evolution of complex limit cycles

2011-06-14

arxiv.org/abs/1106.2786v1

Mathematics

Dynamical Systems

27 pages, submitted to "Discrete and Continuous Dynamical Systems" - Series A

Scientific paper

In the current article we study complex cycles of higher multiplicity in a specific polynomial family of holomorphic foliations in the complex plane. The family in question is a perturbation of an exact polynomial one-form giving rise to a foliation by Riemann surfaces. In this setting, a complex cycle is defined as a nontrivial element of the fundamental group of a leaf from the foliation. In addition to that, we introduce the notion of a multi-fold cycle and show that in our example there exists a limit cycle of any multiplicity. Furthermore, such a cycle gives rise to a one-parameter family of cycles continuously depending on the perturbation parameter. As the parameter decreases in absolute value, the cycles from the continuous family escape from a very large subdomain of the complex plane.

Affiliated with

Also associated with

No associations

Rating

An example of rapid evolution of complex limit cycles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An example of rapid evolution of complex limit cycles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An example of rapid evolution of complex limit cycles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-114301