Skip to main content
SpringerLink
Log in

Schwartzman Cycles and Ergodic Solenoids

  • Chapter
  • First Online:
Essays in Mathematics and its Applications

  • 1371 Accesses

Abstract

We extend Schwartzman theory beyond dimension 1 and provide a unified treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoff’s ergodic theorem for the class of immersions of solenoids with a trapping region.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

References

  1. V. Muñoz, R. Pérez-Marco, Ergodic solenoidal homology II: density of ergodic solenoids. Aust. J. Math. Anal. Appl. 6(1), Article 11, 1–8 (2009)

    Google Scholar 

  2. V. Muñoz, R. Pérez-Marco, Ergodic solenoids and generalized currents. Revista Matemática Complutense 24, 493–525 (2011)

    Google Scholar 

  3. V. Muñoz, R. Perez-Marco, Intersection theory for ergodic solenoids (2009). Arxiv preprint arXiv:0910.2915

    Google Scholar 

  4. V. Muñoz, R. Pérez-Marco, Ergodic solenoidal homology: realization theorem. Commun. Math. Phys. 302, 737–753 (2011)

    Google Scholar 

  5. V. Munoz, R. P. Marco, Hodge theory for Riemannian solenoids. Funct. Equ. Math. Anal. 633–657 (2012). Springer

    Google Scholar 

  6. D. Ruelle, D. Sullivan, Currents, flows and diffeomorphisms. Topology 14, 319–327 (1975)

    Google Scholar 

  7. S. Schwartzman, Asymptotic cycles. Ann. Math. 66(2), 270–284 (1957)

    Google Scholar 

  8. R. Thom, Sous-variétés et classes d’homologie des variétés différentiables. I et II. C. R. Acad. Sci. Paris 236, 453–454, 573–575 (1953)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040, Madrid, Spain

    Vicente Muñoz

  2. Université Paris XIII, 99, Avenue J.-B. Clément, 93430, Villetaneuse, France

    Ricardo Pérez Marco

Authors
  1. Vicente Muñoz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Pérez Marco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vicente Muñoz .

Editor information

Editors and Affiliations

  1. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  2. , Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens, 15780, Greece

    Themistocles M. Rassias

Additional information

Dedicated to the 80th Anniversary of Professor Stephen Smale

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Muñoz, V., Marco, R.P. (2012). Schwartzman Cycles and Ergodic Solenoids. In: Pardalos, P., Rassias, T. (eds) Essays in Mathematics and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28821-0_13

Download citation

Publish with us

Policies and ethics

Search

Navigation