Skip to main content
SpringerLink
Log in

Sectional-Anosov flows on certain compact 3-manifolds

  • Published:
Bulletin of the Brazilian Mathematical Society, New Series Aims and scope Submit manuscript

Abstract

A sectional-Anosov flow is a flow for which the maximal invariant set is sectional-hyperbolic. A generalized 3-handlebody is a compact manifold which is built from a 3-disc attaching 0, 1, 2 and 3-handles at its boundary, one at a time, by attaching maps. We prove that there exist a class of orientable generalized 3-handlebodies supporting sectional-Anosov flows, moreover this class of manifolds is strictly large than the previous one studied in [14].

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Afraimovich, V.V. Bykov and L.P. Shilnikov. On attracting structurally unstable limit sets of Lorenz attractor type. Tr. Mosk. Mat. Obshch., 44 (1982), 150–212.

    MathSciNet  Google Scholar 

  2. V. Afraimovich and S.-B. Hsu. Lectures on chaotic dynamical systems. AMS/IP Stud. Adv. Math. 28, Amer. Math. Soc., Providence, Rhode Island (2003).

    MATH  Google Scholar 

  3. D.V. Anosov. Geodesic flows on closed Eiemann manifolds with negative curvature. Proceedings of the Steklov Institute of Mathematics, 90 (1967).

  4. S. Bautista and C. Morales. Lectures on sectional-Anosov flows, preprint (2010).

  5. H.G. Bothe. Strange attactors with topologically simple basins. Topology Appl., 114(1) (2010), 1–25.

    Article  MathSciNet  Google Scholar 

  6. W. de Melo and J. Palis. Geometric theory of dynamical systems. An introduction. Springer-Verlag, New York-Berlin (1982).

    MATH  Google Scholar 

  7. A. Douady. Arrondissement des Arêtes. Sem. H. Cartan, 14(3) (1961/62).

  8. J. Franks and R. Willians. Anomalous Anosov flows. Global theory of dynamical systems. Proc. Internat. Conf., Northwestern Univ., Evanston, III, 158–174(1979).

    Google Scholar 

  9. J. Guckenheimer and R.F. Williams. Structural stability of Lorenz attractors. Inst. Hautes Etudes Sci. Publ. Math., 50 (1979), 59–72.

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Handel and W. Thurston. Anosov flows on new three manifolds. Invent. Math., 2 (1980), 95–103.

    Article  MathSciNet  Google Scholar 

  11. M. Hirsch, C. Pugh and M. Shub. Invariant Manifolds. Lec. Not. in Math., 583, Springer-Verlag (1977).

  12. Y. Matsumoto. An Introduction to Morse Theory. Translations of Math. Monographs, 208 (2002).

  13. R. Metzger and C. Morales. Sectional-hyperbolic systems. Ergodic Theory Dynam. Systems, 28 (2008), 1587–1597.

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Morales. Singular-Hyperbolic Attractors With Handlebody Basins. Journal of Dynamical and Control Systems, 13(1) (2007), 15–24.

    Article  MathSciNet  MATH  Google Scholar 

  15. L.I. Nicolaescu. An Invitation to Morse Theory. Springer Universitext (2007).

Download references

Author information

Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box: 68530, 21945-970, Rio de Janeiro, Brazil

    Tatiana Sodero

Authors
  1. Tatiana Sodero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatiana Sodero.

Additional information

The author was supported by CNPq.

About this article

Cite this article

Sodero, T. Sectional-Anosov flows on certain compact 3-manifolds. Bull Braz Math Soc, New Series 42, 439–454 (2011). https://doi.org/10.1007/s00574-011-0024-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00574-011-0024-5

Keywords

Mathematical subject classification

Search

Navigation