Have a personal or library account? Click to login
Orbital shadowing property on chain transitive sets for generic diffeomorphisms Cover

Orbital shadowing property on chain transitive sets for generic diffeomorphisms

By: Manseob Lee  
Open Access
|Jul 2020

References

  1. [1] F. Abdenur, C. Bonatti and S. Crovisier, Nonuniform hyperbolicty for C1-generic diffeomorphisms, Isral J. Math., 183 (2011), 1–60.10.1007/s11856-011-0041-5
  2. [2] F. Abdenur, C. Bonatti and L. J. Díaz, Non-wandering sets with non empty interior, Noinearity, 17 (2004), 175–191.10.1088/0951-7715/17/1/011
  3. [3] F. Abdenur and L. J. Díaz, Pseudo-orbit shadowing in the C1-topology, Discrete Contin. Dyn. Syst., 17 (2) (2007), 223–245.10.3934/dcds.2007.17.223
  4. [4] J. Ahn, K. Lee and M. Lee, Homoclinic classes with shadowing, J. Inequal. Appl., 2012:97 (2012), 1–6.10.1186/1029-242X-2012-97
  5. [5] C. Bonatti and S. Crovisier, Récurrence et généricité, Invent. Math., 158 (2004), 33–104.10.1007/s00222-004-0368-1
  6. [6] C. Bonatti and L. J. Díaz, Robust heterodimensional cycles and C1 generic dynamics, J. Inst. Math. Jessieu, 7 (2008), 469–525.
  7. [7] C. Carballo, C. A. Morales and M. J. Pcaifico, Homoclinic classes for C1 generic vector fields, Ergod. Theorey Dynam. Syst., 23 (2003), 403–415.
  8. [8] S. Crovisier, Periodic orbits and chain transitive sets of C1-diffeo-morphisms, Publ. Math. Inst. Hautes Etudes. Sci., 104 (2006), 87–141.10.1007/s10240-006-0002-4
  9. [9] K. Lee and M. Lee, Shadowable chain recurrence classes for generic diffeomorphisms, Taiwan J. Math., 20 (2016), 399–409.
  10. [10] K. Lee and M. Lee, Volume preserving diffeomorphisms with orbital shadowing, J. Inequal. Appl., 2013:18, (2013), 5 pp.10.1186/1029-242X-2013-18
  11. [11] K. Lee and X. Wen, Shadowable chain transitive sets of C1 generic diffeomorphisms, Bull. Korean Math. Soc.49 (2012), 263–270.10.4134/BKMS.2012.49.2.263
  12. [12] M. Lee, Hamiltonian systems with orbital, orbital inverse shadowing, Adv. Difference Equ., 2014:192(2014), 9 pp.10.1186/1687-1847-2014-192
  13. [13] M. Lee, Orbital shadowing property for generic divergence-free vector fields, Chaos Solitons & Fractals, 54 (2013), 71–75.10.1016/j.chaos.2013.05.013
  14. [14] M. Lee, Orbital shadowing for C1-generic volume-preserving diffeomorphisms, Abstr. Appl. Anal., 2013, Art. ID 693032, 4 pp.10.1155/2013/693032
  15. [15] M. Lee, Divergence-free vector fields with orbital shadowing, Adv. Difference Equ, 2013:132, (2013), 6 pp.10.1186/1687-1847-2013-132
  16. [16] M. Lee, Robustly chain transitive sets with orbital shadowing diffeomorphisms, Dyn. Syst., 27 (2012), 507–514.10.1080/14689367.2012.725032
  17. [17] M. Lee, Chain components with C1-stably orbital shadowing, Adv. Difference Equ., 2013:67 (2013), 12 pp.10.1186/1687-1847-2013-255
  18. [18] M. Lee, Chain transitive sets with dominated splitting, J. Math. Sci. Adv. Appl., 4 (2010), 201–208.
  19. [19] A. V. Osipov, Nondensity of the orbital shadowing property in C1-topology, (Russian) Algebra i Analiz 22 (2010), no. 2, 127–163; translation in St. Petersburg Math. J., 22 (2) (2011), 267–292.
  20. [20] S. Y. Pilyugin, A. A. Rodionova and K. Sakai, Orbital and weak shadowing properties, Discrete Contin. Dyn. Syst., 9 (2) (2003), 287–308.10.3934/dcds.2003.9.287
  21. [21] R. Potrie, Generic bi-Lyapunov stable homoclinic classes, Nonlinearity, 23 (2010), 1631–1649.10.1088/0951-7715/23/7/006
  22. [22] C. Robinson, Stability theorem and hyperbolicity in dynamical systems, Rocky Mountain J. Math., 7 (1977), 425–437.10.1216/RMJ-1977-7-3-425
  23. [23] K. Sakai, Sahdowable chain transitive sets, J. Diff. Eqaut. Appl., 19 (2013), 1601–1618.10.1080/10236198.2013.767897
  24. [24] K. Sakai, Pseudo orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math., 31 (1994), 373–386.
Language: English
Page range: 146 - 154
Submitted on: Sep 18, 2018
|
Published on: Jul 16, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Manseob Lee, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.