JOURNAL BROWSE
Search
Advanced SearchSearch Tips
STRUCTURAL STABILITY OF VECTOR FIELDS WITH ORBITAL INVERSE SHADOWING
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
STRUCTURAL STABILITY OF VECTOR FIELDS WITH ORBITAL INVERSE SHADOWING
Lee, Keon-Hee; Lee, Zoon-Hee; Zhang, Yong;
  PDF(new window)
 Abstract
In this paper, we give a characterization of the structurally stable vector fields via the notion of orbital inverse shadowing. More precisely, it is proved that the interior of the set of vector fields with the orbital inverse shadowing property coincides with the set of structurally stable vector fields. This fact improves the main result obtained by K. Moriyasu et al. in [15].
 Keywords
flow;method;orbital inverse shadowing;shadowing;structurally stable;vector field;
 Language
English
 Cited by
1.
Divergence-free vector fields with inverse shadowing, Advances in Difference Equations, 2013, 2013, 1, 337  crossref(new windwow)
2.
Asymptotic Average Shadowing Property and Chain Transitivity for Multiple Flow Systems, Differential Equations and Dynamical Systems, 2016  crossref(new windwow)
3.
Hamiltonian systems with orbital, orbital inverse shadowing, Advances in Difference Equations, 2014, 2014, 1, 192  crossref(new windwow)
 References
1.
T. Choi, K. Lee, and M. Lee, Inverse shadowing for suspension flows, preprint

2.
R. Corless and S. Pilyugin, Approximate and real trajectories for generic dynamical systems, J. Math. Anal. Appl. 189 (1995), no. 2, 409-423 crossref(new window)

3.
P. Diamond, K. Lee, and Y. Han, Bishadowing and hyperbolicity, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 12 (2002), no. 8, 1779-1788 crossref(new window)

4.
S. Gan and L. Wen, Nonsingular star flows satisfy Axiom A and the no-cycle condition, Invent. Math. 164 (2006), no. 2, 279-315 crossref(new window)

5.
Y. Han and K. Lee, Inverse shadowing for structurally stable flows, Dyn. Syst. 19 (2004), no. 4, 371-388 crossref(new window)

6.
S. Hayashi, On the solution of $C^{1}$ stability conjecture for flows, Ann. Math. 353 (1997), 3391-3408

7.
P. Kloeden and J. Ombach, Hyperbolic homeomorphisms and bishadowing, Ann. Polon. Math. 65 (1997), no. 2, 171-177

8.
P. Kloeden, J. Ombach, and A. Pokrovskii, Continuous and inverse shadowing, Funct. Differ. Equ. 6 (1999), no. 1-2, 137-153

9.
K. Lee, Continuous inverse shadowing and hyperbolicity, Bull. Austral. Math. Soc. 67 (2003), no. 1, 15-26 crossref(new window)

10.
K. Lee and Z. Lee, Inverse shadowing for expansive flows, Bull. Korean Math. Soc. 40 (2003), no. 4, 703-713 crossref(new window)

11.
K. Lee and J. Park, Inverse shadowing of circle maps., Bull. Austral. Math. Soc. 69 (2004), no. 3, 353-359 crossref(new window)

12.
K. Lee and K. Sakai, Various shadowing properties and their equivalence, Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 533-540 crossref(new window)

13.
K. Lee, Structural stability of vector fields with shadowing, J. Differential Equations 232 (2007), no. 1, 303-313 crossref(new window)

14.
R. Mane, A proof of the $C^{1}$ stability conjecture, Inst. Hautes Etudes Sci. Publ. Math. No. 66 (1988), 161-210

15.
K. Moriyasu, K. Sakai, and N. Sumi, Vector fields with topological stability, Trans. Amer. Math. Soc. 353 (2001), no. 8, 3391-3408 crossref(new window)

16.
K. Moriyasu, K. Sakai, and W. Sun, $C^{1}$ stably expansive flows, J. Differential Equations 213 (2005), no. 2, 352-367 crossref(new window)

17.
S. Pilyugin, Shadowing in structurally stable flows, J. Differential Equations 140 (1997), no. 2, 238-265 crossref(new window)

18.
S. Pilyugin, Inverse shadowing by continuous methods, Discrete Contin. Dyn. Syst. 8 (2002), no. 1, 29-38 crossref(new window)

19.
S. Pilyugin, A. Rodionova, and K. Sakai, Orbital and weak shadowing properties, Discrete Contin. Dyn. Syst. 9 (2003), no. 2, 287-308 crossref(new window)

20.
O. Plamenevskaya, Pseudo-orbit tracing property and limit shadowing property on a circle, Vestnik St. Petersburg Univ. Math. 30 (1997), no. 1, 27-30

21.
C. Robinson, Structural stability of vector fields, Ann. of Math. (2) 99 (1974), 154-175 crossref(new window)

22.
C. Robinson, Stability theorems and hyperbolicity in dynamical systems, Rocky Mountain J. Math. 7 (1977), no. 3, 425-437 crossref(new window)

23.
K. Sakai, Pseudo orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math. 31 (1994), no. 2, 373-386

24.
R. Thomas, Topological stability: some fundamental properties, J. Differential Equations 59 (1985), no. 1, 103-122 crossref(new window)

25.
L. Wen, On the $C^{1}$ stability conjecture for flows, J. Differential Equations 129 (1996), no. 2, 334-357 crossref(new window)

26.
K. Yano, Topologically stable homeomorphisms of the circle, Nagoya Math. J. 79 (1980), 145-149