Skip to main content

Part of the book series: Modern Birkhäuser Classics ((MBC,volume 164))

  • 420 Accesses

Abstract

In this chapter, (X λ) will be a smooth or analytic (in Section 3) family of vector fields on a phase space S, with parameter λ ∈ P, as in Chapter 1. Periodic orbits and elliptic singular points which are limits of sequences of limit cycles are called regular limit periodic sets. The reason for this terminology is that for such a limit periodic set r one can define local return maps on transversal segments, which are as smooth as the family itself. The limit cycles near r will be given by a smooth equation and the theory of bifurcations of limit cycles from r will reduce to the theory of unfoldings of differentiable functions. In fact, we will just need the Preparation Theorem and not the whole Catastrophe Theory to treat finite codimension unfoldings.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Basel AG

About this chapter

Cite this chapter

Roussarie, R. (1998). Bifurcations of Regular Limit Periodic Sets. In: Bifurcation of Planar Vector Fields and Hilbert’s Sixteenth Problem. Modern Birkhäuser Classics, vol 164. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8798-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8798-4_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9778-5

  • Online ISBN: 978-3-0348-8798-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics