Diffeomorphisms with weak shadowing

• Autorzy: Kazuhiro Sakai
• Języki publikacji: EN

Abstrakty

EN

The weak shadowing property is really weaker than the shadowing property. It is proved that every element of the C¹ interior of the set of all diffeomorphisms on a $C^{∞}$ closed surface having the weak shadowing property satisfies Axiom A and the no-cycle condition (this result does not generalize to higher dimensions), and that the non-wandering set of a diffeomorphism f belonging to the C¹ interior is finite if and only if f is Morse-Smale.

Kategorie tematyczne

• 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
• 37D15: Morse-Smale systems
• 37C75: Stability theory
• 37B99: None of the above, but in this section
• 37C50: Approximate trajectories (pseudotrajectories, shadowing, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 168
• Numer: 1
• Strony: 57-75

Daty

wydano

2001

Twórcy

autor

Kazuhiro Sakai

• Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Identyfikatory

DOI

10.4064/fm168-1-2