Publication Cover
Dynamical Systems
An International Journal
Volume 27, 2012 - Issue 4
88
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Robustly chain transitive sets with orbital shadowing diffeomorphisms

Pages 507-514 | Received 27 Oct 2011, Accepted 20 Aug 2012, Published online: 24 Sep 2012

References

  • Mãné , R . 1982 . An ergodic closing lemma . Ann. Math. , 116 : 503 – 540 .
  • Díaz , LJ , Pujals , ER and Ures , R . 1999 . Partial hyperbolicity and robustly transitivity . Acta Math. , 183 : 1 – 43 .
  • Bonatti , C , Díaz , LJ and Pujals , ER . 2003 . A C 1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources . Ann. Math. , 158 : 355 – 418 .
  • Arbieto , A and Ribeiro , R . 2011 . Flows with the (asymptotic) average shadowing property on three-dimensional closed manifolds . Dyn. Syst. , 26 : 425 – 432 .
  • Bonatti , C , Li , M and Yang , D . A robustly chain transitive attractor with singularities of different indices , to appear in J. Inst. Math. Jessieu
  • Crovisier , C . Peirodic orbits and chain transitive sets of C 1 diffeomorphisms . Publ. Math. de L'iheś , 104 87 – 141 .
  • Mãné , R . 1978 . Contributions to stability conjecture . Topology , 17 : 383 – 396 .
  • Bonatti , C and Díaz , LJ . 1995 . Persistence of transitive diffeomorphisms . Ann. Math. , 143 : 367 – 396 .
  • Carvalho , M . 1993 . Sinai–Ruelle–Bowen measures for N-dimensional derived from Anosov diffeomorphisms . Ergodic Theory Dyn. Syst. , 13 : 21 – 44 .
  • Shub , M . 1971 . “ Topologically transitive diffeomorphism of 𝕋4 ” . In Symposium on Differential Equations and Dyanmical Systems (University of Warwick, 1968/69), Lecture Notes in Mathematics , Vol. 206 , 39 – 40 . Berlin, New York : Springer-Verlag .
  • Pilyugin , SY . 1999 . Shadowing in Dynamical Systems, Lecture Notes in Mathematics , Vol. 1706 , Berlin : Springer Verlag .
  • Robinson , C . 1977 . Stability theorems and hyperbolicity in dynamical systems . Rocky Mt. J. Math. , 7 : 425 – 437 .
  • Sakai , K . 1994 . Pseudo orbit tracing property and strong transversality of diffeomorphisms on closed manifolds . Osaka J. Math. , 31 : 373 – 386 .
  • Pilyugin , SY , Rodionova , AA and Sakai , K . 2003 . Orbital and weak shadowing properties . Discrete Contin. Dyn. Syst. , 9 : 287 – 308 .
  • Sakai , K , Sumi , N and Yamamoto , K . 2010 . Diffeomorphisms satisfying the specification property . Proc. Am. Math. Soc. , 138 : 315 – 321 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.