Far East Journal of Dynamical Systems
Volume 4, Issue 2, Pages 97 - 106
(December 2002)
|
|
A NOTE ON MAÑÉ’S PROOF OF THE
STABILITY CONJECTURE
Kazumine Moriyasu (Japan) and Kazuhiro Sakai (Japan)
|
Abstract: In his proof of the stability conjecture, Mañé proved that there exists a dominated splitting for and that if is contracting, then is expanding. However, it seems that in the proof of the latter result, there exists a shortage of proof. In this note, we add some arguments to the proof and fill up the shortage for completeness. |
Keywords and phrases: stability conjecture, dominated splitting, shadowing property, Axiom A, no-cycle condition. |
|
Number of Downloads: 287 | Number of Views: 931 |
|