Skip to main content

Linearization

  • Chapter
  • First Online:
Ergodic Theory and Dynamical Systems

Part of the book series: Universitext ((UTX))

  • 3914 Accesses

Abstract

To study the dynamics of a transformation f on a space X, we can try to conjugate f to a simpler model A: Y → Y via a homeomorphism φ: X → Y satisfying Aφ = φf.

I specifically remember discussions among ourselves and with visitors about what is now known as nonlinear mathematics—truly a strange expression, for it is like saying “I will discuss nonelephant animals”.

S. Ulam (1909–1984)

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
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

Institutional subscriptions

References

  1. Arnol′d, V.I., Avez, A.: Ergodic Problems of Classical Mechanics. W.A. Benjamin Inc., New York (1968)

    Google Scholar 

  2. Dudley, R.M.: Real Analysis and Probability. Cambridge Studies in Advanced Mathematics, vol. 74. Cambridge University Press, Cambridge (1989)

    Google Scholar 

  3. Federer, H.: Geometric Measure Theory. Grundlehren der mathematischen Wissenschaften, vol. 153. Springer, New York (1969)

    Google Scholar 

  4. Katok, A., Hasselblatt, B.: Introduction to the Modern Theory of Dynamical Systems. Encyclopedia of Mathematics and Its Applications, vol. 54. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  5. Palis, J., de Melo, W.: Geometric Theory of Dynamical Systems. An Introduction. Springer, Berlin (1982)

    Google Scholar 

  6. Shub, M.: Global Stability of Dynamical Systems. Springer, New York (1987)

    Google Scholar 

  7. Sinaĭ, Y.G.: Topics in Ergodic Theory. Princeton Mathematical Series, vol. 44. Princeton University Press, Princeton, NJ (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag London

About this chapter

Cite this chapter

Coudène, Y. (2016). Linearization. In: Ergodic Theory and Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7287-1_8

Download citation

Publish with us

Policies and ethics