1 |
A. Arroyo and F. R. Hertz, Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows, Ann. Inst. H. Poincare Anal. Non Lineaire 20 (2003), no. 5, 805-841.
DOI
ScienceOn
|
2 |
C. Bonatti, N. Gourmelon, and T. Vivier, Perturbations of the derivative along periodic orbits, Ergodic Theory Dynam. Systems 26 (2006), no. 5, 1307-1337.
DOI
ScienceOn
|
3 |
C. I. Doering, Persistently transitive vector fields on three-dimensional manifolds, Dynamical systems and bifurcation theory (Rio de Janeiro, 1985), 59-89, Pitman Res. Notes Math. Ser., 160, Longman Sci. Tech., Harlow, 1987.
|
4 |
S. Gan, K. Sakai, and L. Wen, -stably weakly shadowing homoclinic classes admit dominated splitting, Discrete Contin. Dyn. Syst. 27 (2010), no. 1, 205-216.
DOI
|
5 |
S. Gan and L. Wen, Nonsingular star flows satisfy Axiom A and the no-cycle condition, Invent. Math. 164 (2006), no. 2, 279-315.
DOI
|
6 |
N. Gourmelon, A Franks' lemma that preserves invariant manifolds, preprint at http://www.preprint.impa.br/.
|
7 |
S. Hayashi, Connecting invariant manifolds and the solution of the -stability and -stability conjectures for flows, Ann. of Math. (2) 145 (1997), no. 1, 81-137.
DOI
|
8 |
M. Komuro, One-parameter flows with the pseudo orbit tracing property, Monatsh. Math. 98 (1984), no. 3, 219-253.
DOI
|
9 |
M. Li, S. Gan, and L. Wen, Robustly transitive singular sets via approach of an extended linear Poincare flow, Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 239-269.
DOI
|
10 |
S. Liao, An existence theorem for periodic orbits, Acta. Sci. Nat. Univ. Pekin. 1 (1979), 1-20.
|
11 |
K. Lee and M. Lee, Hyperbolicity of -stably expansive homoclinic classes, Discrete Contin. Dyn. Syst. 27 (2010), no. 3, 1133-1145.
DOI
|
12 |
K. Lee, K. Moriyasu, and K. Sakai, -stable shadowing diffeomorphisms, Discrete Contin. Dyn. Syst. 23 (2008), no. 3, 683-697.
|
13 |
K. Lee and K. Sakai, Structural stability of vector fields with shadowing, J. Differential Equations 232 (2007), no. 1, 303-313.
DOI
ScienceOn
|
14 |
R. Mane, An ergodic closing lemma, Ann. of Math. (2) 116 (1982), no. 3, 503-540.
DOI
ScienceOn
|
15 |
J. Palis and W. de Melo, Geometric Theory of Dynamical Systems: An Introduction, Springer-Verlag, 1982.
|
16 |
C. Pugh and C. Robinson, The closing lemma, including Hamiltonians, Ergodic Theory Dynam. Systems 3 (1983), no. 2, 261-313.
|
17 |
S. Yu. Pilyugin and S. B. Tikhomirov, Vector fields with the oriented shadowing property, J. Differential Equations 248 (2010), no. 6, 1345-1375.
DOI
ScienceOn
|
18 |
C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, Second edition, Studies in Advanced Mathematics, CRC Press, 1999.
|
19 |
K. Sakai, Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math. 31 (1994), no. 2, 373-386.
|
20 |
K. Sakai, -stably shadowable chain components, Ergodic Theory Dynam. Systems 28 (2008), no. 3, 987-1029.
|
21 |
M. Sambarino and J. L. Vieitez, On -persistently expansive homoclinic classes, Discrete Contin. Dyn. Syst. 14 (2006), no. 3, 465-481.
|
22 |
X. Wen, S. Gan, and L. Wen, -stably shadowable chain components are hyperbolic, J. Differential Equations 246 (2009), no. 1, 340-357.
DOI
ScienceOn
|