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STRUCTURAL STABILITY OF VECTOR FIELDS WITH ORBITAL INVERSE SHADOWING

  • Lee, Keon-Hee (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY) ;
  • Lee, Zoon-Hee (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY) ;
  • Zhang, Yong (DEPARTMENT OF MATHEMATICS SUZHOU UNIVERSITY)
  • Published : 2008.11.01

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 $C^1$ interior of the set of $C^1$ 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

References

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  2. Divergence-free vector fields with inverse shadowing vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1847-2013-337
  3. Hamiltonian systems with orbital, orbital inverse shadowing vol.2014, pp.1, 2014, https://doi.org/10.1186/1687-1847-2014-192