scholarly journals STRUCTURAL STABILITY OF VECTOR FIELDS WITH ORBITAL INVERSE SHADOWING

2008 ◽  
Vol 45 (6) ◽  
pp. 1505-1521 ◽  
Author(s):  
Keon-Hee Lee ◽  
Zoon-Hee Lee ◽  
Yong Zhang
Keyword(s):  
Structural Stability ◽  
Vector Fields ◽  
Inverse Shadowing ◽  
Orbital Inverse Shadowing

scholarly journals Characterisations of Ω-stability and structural stability via inverse shadowing

2006 ◽  
Vol 74 (2) ◽  
pp. 185-196 ◽  
Author(s):  
Taeyoung Choi ◽  
Keonhee Lee ◽  
Yong Zhang
Keyword(s):  
Structural Stability ◽  
Shadowing Property ◽  
Inverse Shadowing ◽  
Orbital Inverse Shadowing ◽  
Structurally Stable

We give characterisations of Ω-stable diffeomorphisms and structurally stable diffeomorphisms via the notions of weak inverse shadowing and orbital inverse shadowing, respectively. More precisely, it is proved that the C1 interior of the set of diffeomorphisms with the weak inverse shadowing property coincides with the set of Ω-stable diffeomorphisms and the C1 interior of the set of diffeomorphisms with the orbital inverse shadowing property coincides with the set of structurally stable diffeomorphisms.

Structural stability of planar quasi-homogeneous vector fields

2018 ◽  
Vol 468 (1) ◽  
pp. 212-226 ◽  
Author(s):  
A. Algaba ◽  
N. Fuentes ◽  
E. Gamero ◽  
C. Garcia
Keyword(s):  
Structural Stability ◽  
Vector Fields ◽  
Homogeneous Vector Fields ◽  
Homogeneous Vector

scholarly journals Continuous inverse shadowing and hyperbolicity

2003 ◽  
Vol 67 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Keonhee Lee
Keyword(s):  
Structural Stability ◽  
Inverse Shadowing ◽  
Continuous Inverse

We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.

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