Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity

Details Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity

2012-02-06

arxiv.org/abs/1202.1179v1

Mathematics

Dynamical Systems

Scientific paper

In this paper we prove the breakdown of an heteroclinic connection in the analytic versal unfoldings of the generic Hopf-Zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order if one performs the normal form around the origin, therefore it is a phenomenon "beyond all orders". In this paper we provide a formula for the distance between the corresponding stable and unstable one dimensional manifolds which is given by an exponentially small function in the perturbation parameter. Our result applies both for conservative and dissipative unfoldings.

Affiliated with

Also associated with

No associations

Rating

Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity 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 Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-119734