Advertisement

Limit Periodic Sets

Chapter
  • 240 Downloads
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

As explained at the end of the previous chapter, the most difficult problem in the study of bifurcations in a family of vector fields on a surface of genus 0 is the control of the periodic orbits. In fact, in generic smooth families the periodic orbits will be isolated for each value of the parameter. For analytic families we have two possibilities for each orbit: it may be isolated or belong to a whole annulus of periodic orbits. In this last case and for the parameter values for which the system has infinitely many periodic orbits, the vector field has a local analytic first integral and the nearby vector fields in the family may be studied by the perturbation theory introduced in Chapter 4. They have in general isolated periodic orbits. The interest in the study of isolated periodic orbits is also justified by tradition and by applications.

Keywords

Periodic Orbit Singular Point Elementary Graphic Polynomial Vector Regular Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel 1998

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BourgogneDijon CedexFrance

Personalised recommendations