Skip to main content

The Deployment Theorem

  • Chapter
  • First Online:
  • 697 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2214))

Abstract

The main result of this chapter is that a minimal rotation set for m d is uniquely determined by its rotation number together with an invariant called the “deployment vector” which, roughly speaking, describes how the points of the rotation set are deployed relative to the d − 1 fixed points of m d .

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

Buying options

eBook
USD   19.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   29.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Notes

  1. 1.

    In the terminology of [11], the integers s i define the deployment sequence of X.

References

  1. L. Goldberg, Fixed points of polynomial maps I: rotation subsets of the circles. Ann. Sci. École Norm. Sup. 25, 679–685 (1992)

    Article  MathSciNet  Google Scholar 

  2. L. Goldberg, C. Tresser, Rotation orbits and the Farey tree. Ergodic Theory Dyn. Syst. 16, 1011–1029 (1996)

    Article  MathSciNet  Google Scholar 

  3. C. McMullen, Dynamics on the unit disk: short geodesics and simple cycles. Comment. Math. Helv. 85, 723–749 (2010)

    Article  MathSciNet  Google Scholar 

  4. C. Petersen, S. Zakeri, On combinatorial types of periodic orbits of the map \(x \mapsto kx \ (\operatorname {mod} \ {\mathbb Z})\). Part I: Realization. arXiv:1712.04506

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zakeri, S. (2018). The Deployment Theorem. In: Rotation Sets and Complex Dynamics. Lecture Notes in Mathematics, vol 2214. Springer, Cham. https://doi.org/10.1007/978-3-319-78810-4_3

Download citation

Publish with us

Policies and ethics