C0 transversality and shadowing properties

Proceedings of the Steklov Institute of Mathematics

Volumn 256, Issue 1, 2007, Pages 290-305

  Pilyugin, S Yu ^a   Sakai, K ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UTSUNOMIYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34248333471     PISSN: 00815438     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0081543807010178     Document Type: Article

References (20)

1. D. V. Anosov, "On a Class of Invariant Sets of Smooth Dynamical Systems," in Proc. 5th Int. Conf. on Nonlinear Oscillations (Inst. Math. Acad. Sci. Ukr. SSR, Kiev, 1970), Vol. 2, pp. 39-45.
2. R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms (Springer, Berlin, 1975), Lect. Notes Math. 470.
3. S. Yu. Pilyugin, Shadowing in Dynamical Systems (Springer, Berlin, 1999), Lect. Notes Math. 1706.
4. K. Palmer, Shadowing in Dynamical Systems: Theory and Applications (Kluwer, Dordrecht, 2000).
5. C. Robinson, "Stability Theorems and Hyperbolicity in Dynamical Systems," Rocky Mt. J. Math. 7, 425-437 (1977).
6. A. Morimoto, The Method of Pseudo-orbit Tracing and Stability of Dynamical Systems (Tokyo Univ., Tokyo, 1979), Semin. Note 39.
7. K. Sawada, "Extended f-Orbits Are Approximated by Orbits," Nagoya Math. J. 79, 33-45 (1980).
8. S. Yu. Pilyugin, "Shadowing in Structurally Stable Flows," J. Diff. Eqns. 140, 238-265 (1997).
9. S. Yu. Pilyugin, "Inverse Shadowing by Continuous Methods," Discrete Contin. Dyn. Syst. 8, 29-38 (2002).
10. K. Sakai, "Shadowing Property and Transversality Condition," in Dynamical Systems and Chaos (World Sci., Singapore, 1995), Vol. 1, pp. 233-238.
11. S. Yu. Pilyugin, Introduction to Structurally Stable Systems of Differential Equations (Birkhäuser, Basel, 1992).
12. W. de Melo, "Structural Stability of Diffeomorphisms on Two-Manifolds," Invent. Math. 21, 233-246 (1973).
13. D. V. Anosov, Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature (Nauka, Moscow, 1967), Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 90
14. [Proc. Steklov Inst. Math. 90 (1967)].
15. J. Palis, "On Morse-Smale Dynamical Systems," Topology 8, 385-404 (1969).
16. S. Smale, "Differentiable Dynamical Systems," Bull. Am. Math. Soc. 73, 747-817 (1967).
17. 1 Ω-Stability Conjecture," Publ. Math., Inst. Hautes Étud. Sci. 66, 211-215 (1988).
18. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge Univ. Press, Cambridge, 1995).
19. G. D. Birkhoff, Dynamical Systems (Am. Math. Soc., New York, 1927).
20. 1-Open Sets of Diffeomorphisms with Weak Shadowing," Discrete Contin. Dyn. Syst. 16, 871-882 (2006).