IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-71261-1_2.html
   My bibliography  Save this book chapter

Lyapunov Exponents and Regularity

In: Lyapunov Exponents

Author

Listed:
  • Luís Barreira

    (Universidade de Lisboa, Instituto Superior Técnico)

Abstract

This chapter is an introduction to the basic theory of Lyapunov exponents. We first introduce the notions of a Lyapunov exponent and of Lyapunov regularity in terms of the Grobman coefficient. This is part of what is usually called the abstract theory of Lyapunov exponents. We then illustrate the notions with two specific classes of Lyapunov exponents obtained from a linear dynamics. More precisely, we consider linear dynamics with discrete and continuous time, with the study, respectively, of the Lyapunov exponents defined by sequences of invertible matrices and by nonautonomous linear differential equations. These two classes of Lyapunov exponents are the main objects of study in the book. Finally, we introduce the Perron coefficient and we use it to give an alternative characterization of Lyapunov regularity, in terms of the values of the dual Lyapunov exponents used to define the Grobman coefficient.

Suggested Citation

  • Luís Barreira, 2017. "Lyapunov Exponents and Regularity," Springer Books, in: Lyapunov Exponents, chapter 0, pages 31-41, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-71261-1_2
    DOI: 10.1007/978-3-319-71261-1_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-319-71261-1_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.