Reduction principle in the theory of stability of difference equations

Discrete and Continuous Dynamical Systems- Series A

Volumn , Issue SUPPL., 2007, Pages 864-874

  Reinfelds, Andrejs ^a   Janglajew, Klara ^b  

^a UNIVERSITY OF LATVIA   (Latvia)

^b UNIVERSITY OF BIALYSTOK   (Poland)

Author keywords

Asymptotic phase; Invariant manifold; Reduction principle; Stability of solutions

Indexed keywords

EID: 72149101108     PISSN: 10780947     EISSN: 15535231     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., 90 (1967), in Russian.
2. B. Aulbach, A reduction principle for nonautonomous differential equations, Arch. Mat., 39 (1982), 217-232.
3. J. Carr, "Applications of Centre Manifold Theory," Springer, 1981.
4. J. Hadamard, Sur l'itération et les solutions asymptotiques des équations différentielles, Bull. Soc. Math. France, 29 (1901), 224-228.
5. K. Janglajew, On the reduction principle of difference equations, Dyn. Contin. Discrete Impulsive Syst., 6 (1999), 381-388.
6. O. B. Lykova, The reduction principle in Banach space, Ukrainian Math. J., 23 (1971), 391-397.
7. K. J. Palmer, On the stability of the center manifold, Z. Angew. Math. Phys., 38 (1987), 273-278.
8. V. A. Pliss, A reduction principle in the theory of stability of motion, Izv. Akad. Nauk SSSR Ser. Mat., 28 (1964), 1297-1324 (Russian).
9. Ch. Pötzcsche, Slow and fast variables in non-autonomous difference equations, J. Difference Equ. Appl., 9 (2003), 473-487.
10. A. Reinfelds, The stability of semidynamical system in metric space, Latv. Univ. Zināt. Raksti, 599 (1995), 140-145.
11. A. Reinfelds, The reduction of discrete dynamical and semidynamical systems in metric spaces, in "Six lectures on dynamical systems," (eds. B. Aulbach and F. Colonius), World Sci. Publishing, River Edge, NJ, (1996), 267-312.