Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Sectional Lyapunov exponents

Author: Alexander Arbieto
Journal: Proc. Amer. Math. Soc. 138 (2010), 3171-3178
MSC (2010): Primary 37C10; Secondary 37D25
Published electronically: April 21, 2010
MathSciNet review: 2653942
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We define sectional Lyapunov exponents and use them to characterize sectional Anosov flows in terms of dominated splittings. In particular we improve a result of Sataev.

References [Enhancements On Off] (What's this?)

  • 1. Arnold, L., Random Dynamical Systems. Springer-Verlag, 2003. MR 1374107 (97a:58094)
  • 2. Alves, J., Araújo, V. and Saussol, B., On the uniform hyperbolicity of some nonuniformly hyperbolic systems. Proc. Amer. Math. Soc. 131, no. 4, 1302-1309, 2003. MR 1948124 (2003k:37046)
  • 3. Arbieto, A., Morales, C. and Senos, L., On the sensitivity of Sectional-Anosov Flows. Submitted to Communications on Mathematical Physics, 2009.
  • 4. Bautista, S., Morales, C., Existence of periodic orbits for singular-hyperbolic sets. Mosc. Math. J. 6, no. 2, 265-297, 406, 2006. MR 2270614 (2007m:37075)
  • 5. Bautista, S., Morales, C., Lectures on sectional Anosov flows. Submitted to Memoirs of the AMS, 2009.
  • 6. Bautista, S., Morales, C., Pacifico, M. J., On the intersection of homoclinic classes on singular-hyperbolic sets. Discrete Contin. Dyn. Syst. 19, no. 4, 761-775, 2007. MR 2342271 (2008i:37056)
  • 7. Cao, Y., Non-zero Lyapunov exponents and uniform hyperbolicity. Nonlinearity 16, 1473-1479, 2003. MR 1986306 (2005g:37061)
  • 8. Morales, C., A., Sectional-Anosov systems. Monatsh. Math., to be published.
  • 9. Oseledets, V., A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems. Trudy Moskov. Mat. Obšc. 19, 179-210, 1968. MR 0240280 (39:1629)
  • 10. Sataev, E., Some properties of singular hyperbolic attractors, Math. Sbornik. 200:1, 27-80. 2009. MR 2499676
  • 11. Viana, M., What's new on Lorenz strange attractors?, Math. Intelligencer, 22, no. 3, 6-19, 2000. MR 1773551 (2001h:37068)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37C10, 37D25

Retrieve articles in all journals with MSC (2010): 37C10, 37D25

Additional Information

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

Keywords: Lyapunov exponents, sectional Anosov flows.
Received by editor(s): October 8, 2009
Published electronically: April 21, 2010
Additional Notes: This work was partially supported by CNPq and by Faperj. The author thanks Prof. C. Morales for his useful comments.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society