Diffeomorphisms with C2 stable shadowing

Dynamical Systems

Volumn 17, Issue 3, 2002, Pages 235-241

  Sakai, Kazuhiro ^a  

^a UTSUNOMIYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SET THEORY; TOPOLOGY;

DIFFEOMORPHISMS; HYPERBOLICITY;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0036763609     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/14689360210141941     Document Type: Article

References (12)

1. Bowen, R., 1975, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Vol. 470 (Berlin: Springer-Verlag).
2. de Melo, W., 1973, Structural stability of diffeomorphisms on two-manifolds. Inventiones Mathematicae, 21: 233-246.
3. Franks, J., 1971, Necessary conditions for stability of diffeomorphisms. Transactions of the American Mathematical Society, 158: 301-308.
4. 1 (M) satisfy Axiom. Ergodic Theory and Dynamical Systems, 12: 233-253.
5. Newhouse, S., Palis, J., and Takens, F., 1983, Bifurcations and stability of families of diffeomorphisms. Publications Mathématiques de Institut des Hautes Études, 57: 5-71.
6. Palis, J., and Takens, F., 1993, Hyperbolicity and Sensitive-chaotic Dynamics at Homoclinic Bifurcations (Cambridge: Cambridge University Press).
7. Pilyugin, S. Yu., 1999, Shadowing in Dynamical Systems, Lecture Notes in Mathematics, Vol. 1706 (Berlin: Springer-Verlag).
8. Pujals, E. R., and Sambarino, M., 2000, Homoclinic tangencies and hyperbolicity for surface diffeomorphisms. Annals of Mathematics, 151: 961-1023.
9. Ruelle, D., and Takens, F., 1971, On the nature of turbulence. Communications in Mathematical Physics, 20: 167-192.
10. Sakai, K., 1994, Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds. Osaka Journal of Mathematics, 31: 373-386.
11. Sakai, K., 1995, Shadowing property and transversality condition. Proceedings of the International Conference on Dynamical Systems and Chaos, Tokyo, 1994, Vol. 1 (Singapore: World Scientific), pp. 233-238.
12. Sakai, K., 1996, Diffeomorphisms with the shadowing property. Journal of the Australian Mathematical Society (Series A), 61: 396-399.