Diffeomorphisms with weak shadowing

Kazuhiro Sakai. "Diffeomorphisms with weak shadowing." Fundamenta Mathematicae 168.1 (2001): 57-75. <http://eudml.org/doc/282366>.

@article{KazuhiroSakai2001,
abstract = {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.},
author = {Kazuhiro Sakai},
journal = {Fundamenta Mathematicae},
keywords = {pseudo-orbits; weak shadowing property; shadowing property; Morse-Smale; Axiom A; no-cycle condition; strong transversality condition; structurally stable},
language = {eng},
number = {1},
pages = {57-75},
title = {Diffeomorphisms with weak shadowing},
url = {http://eudml.org/doc/282366},
volume = {168},
year = {2001},
}

TY - JOUR
AU - Kazuhiro Sakai
TI - Diffeomorphisms with weak shadowing
JO - Fundamenta Mathematicae
PY - 2001
VL - 168
IS - 1
SP - 57
EP - 75
AB - 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.
LA - eng
KW - pseudo-orbits; weak shadowing property; shadowing property; Morse-Smale; Axiom A; no-cycle condition; strong transversality condition; structurally stable
UR - http://eudml.org/doc/282366
ER -