45 research outputs found
Singular hyperbolicity of generic three dimensional vector fields
In the paper, we show that for a generic vector field on a closed
three dimensional manifold , any isolated transitive set of is singular
hyperbolic. It is a partial answer of the conjecture in \cite{MP}.Comment: 20pag
C
Let f be a diffeomorphism on a C∞ closed surface. In this paper, we show that if f has the C2-stably limit shadowing property, then we have the following: (i) f satisfies the Kupka-Smale condition; (ii) if P(f) is dense in the nonwandering set Ω(f) and if there is a dominated splitting on Ps(f), then f satisfies both Axiom A and the strong transversality condition
Stable weakly shadowable volume-preserving systems are volume-hyperbolic
We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are
volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a
consequence, in low dimensions, we obtain global hyperbolicity.info:eu-repo/semantics/publishedVersio