Connections between Morse sets for delay-differential equations

Journal fur die Reine und Angewandte Mathematik

Volumn 1989, Issue 397, 1989, Pages 23-41

  Fiedler, Bernold ^a   Mallet Paret, John ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001852665     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1989.397.23     Document Type: Article

References (21)

1. S. Angenent, The Morse-Smale property for a semilinear parabolic equation, J. Diff. Eq. 62 (1986), 427—442.
2. S. Angenent and B. Fiedler, The dynamics of rotating waves in scalar reaction diffusion equations, Trans. Amer. Math. Soc. 307 (1988), 545—568.
3. J. E. Billotti and J. P. LaSalle, Periodic dissipative processes, Bull. Amer. Math. Soc. 6 (1971), 1082—1089.
4. P. Brunovshý and B. Fiedler, Numbers or zeros on invariant manifolds in reaction diffusion equations, Nonl. Analysis TMA 10 (1986), 179—193.
5. P. Brunovshý and B. Fiedler, Connecting orbits in scalar reaction diffusion equations, Dynamics Reported 1 (1988), 57—89.
6. C. C. Conley, Isolated invariant sets and the Morse index, Conf. Board Math. Sci 38, AMS, Providence 1978.
7. K. Deimling, Nonlinear Functional Analysis, Berlin-Heidelberg-New York 1985.
8. J. Dugundi, Topology, Boston 1966.
9. J. D. Farmer, Chaotic attractors of an infinite-dimensional dynamical system, Physica 4D (1982), 366—393.
10. J. K. Hale, Theory of Functional Differential Equations, Berlin-Heidelberg-New York 1977.
11. J. K. Hale, Some recent results on dissipative processes, in: Functional Differential Equations and Bifurcation, Lect. Notes in Math. 799 (1980), 152—172.
12. P. Hartman, On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexicana 5 (1960), 220—241.
13. P. Hartman, Ordinary Differential Equations, Boston, 1982.
14. D. Henry, Some infinite dimensional Morse-Smale systems defined by parabolic equations, J. Diff. Eq. 59 (1985), 165—205.
15. M. W. Hirsch, Differential Topology, Berlin-Heidelberg-New York 1976.
16. W. Hurewicz and H. Wallman, Dimension Theory, Princeton 1948.
17. M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197 (1977), 287—289.
18. J. Mallet-Paret, Morse decompositions and global continuation of periodic solutions for singularly perturbed delay equations, in: Systems of Nonlinear Partial Differential Equations, Dordrecht, (1983), 351—366.
19. J. Mallet-Paret, Morse decompositions for delay-differential equations, J. Diff. Eq. 72 (1988), 270—315.
20. H. Matano, Nonincrease of the lap-number of a solution for a one-dimensional semi-linear parabolic equation, J. Fac. Sci. Univ. Tokyo Sec. IA 29 (1982), 401—441.
21. J. Smoller, Shock Waves and Reaction Diffusion Equations, Berlin-Heidelberg-New York 1983.