IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-56589-2_25.html
   My bibliography  Save this book chapter

Dimension Estimates for Invariant Sets of Dynamical Systems

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author

Listed:
  • Volker Reitmann

    (Fachrichtung Mathematik, Technische Universität Dresden)

Abstract

We investigate the relationships between various types of dimension like characteristics (e.g. Hausdorff, box, and Lyapunov dimensions, topological entropy) of dynamical systems and the geometric complexity of invariant and limit sets (e.g. isolated equilibria, global attracting or unstable cycles, products of Cantor-type sets and regular objects). We consider both flows and discrete-time dynamical systems of smoothness C 1 on n-dimensional smooth Riemannian manifolds which possess compact invariant sets. We formulate our results in terms of the singular values of the linearized evolution operator and consider additionally global informations such as the homology group and curvature properties of the manifold, natural Lyapunov functions and Losinskii norms, and the degree of non-injectivity of the generating map.

Suggested Citation

  • Volker Reitmann, 2001. "Dimension Estimates for Invariant Sets of Dynamical Systems," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 585-615, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_25
    DOI: 10.1007/978-3-642-56589-2_25
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:978-3-642-56589-2_25. 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.