Abstract
We prove that in the set of all C 1 vector fields on a compact manifold there is a residual subset which satisfies the property that if a vector field is Bowen-expansive, then it is Axiom A without cycles.
Similar content being viewed by others
References
A. Arbieto. Periodic Orbits and Expansiveness. To appear in Math. Z. (2010).
R. Bowen and P. Walters. Expansive one-parameter flows. J. Differential Equations, 12 (1972), 180–193.
S. Gan and L. Wen. Nonsingular star flows satisfy Axiom A and the no-cycle condition. Invent. Math., 164(2) (2006), 279–315.
A. Katok and B. Hasselblatt. Introduction to the modern theory of dynamical systems. Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge (1995).
R. Mañé. Expansive diffeomorphisms. Lecture Notesin Math., Vol. 468, Springer, Berlin (1975).
K. Moriyasu, W. Sakai and N. Sun. C 1-stably expansive flows. Journal of Differential Equations, 213 (2005), 352–367.
M. Oka. Expansiveness of real flows. Tsukuba J. Math., 14(1) (1990), 1–8.
S. Gan and D. Yang. Expansive homoclinic classes. Nonlinearity, 22(4) (2009), 729–733.
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by CAPES and CNPq.
About this article
Cite this article
Senos, L. Generic Bowen-expansive flows. Bull Braz Math Soc, New Series 43, 59–71 (2012). https://doi.org/10.1007/s00574-012-0005-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00574-012-0005-3