Spatial chaotic structure of attractors of reaction-diffusion systems

Transactions of the American Mathematical Society

Volumn 348, Issue 12, 1996, Pages 5031-5063

  Afraimovich, V ^a   Babin, A ^b   Chow, S N ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b RUSSIAN UNIVERSITY OF TRANSPORT   (Russian Federation)

Author keywords

Homotopy complexity; Potential; Reaction diffusion system; Symbolic dynamics

Indexed keywords

EID: 21444434271     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01578-4     Document Type: Article

References (18)

1. [A] V. M. Alekseev, Symbolic Dynamics, XI Summer School of Academy of Science of Ukraine, Kiev, Naukova Dumka (1976). MR 57:4249
2. [AC] V. S. Afraimovich and S.-N. Chow, Criteria of spatial chaos in lattice dynamical systems, Preprint CDSNS 93-142 (1993).
3. [ACZ] A. Ambrosetti, V. Coti-Zelati, Closed orbits of fixed energy for singular Hamiltonian systems, Arch. Rat. Mech. Anal. 112 (1990), 339-362. MR 91k:34053
4. [BBH] F. Bethuel, N. Brezis and F. Helein, Ginzburg-Landau Vortices, Birkhäuser, 1994. MR 95c:58044
5. [BV] A. V. Babin, M. I. Vishik, Attractors of Evolution Equations, North-Holland, 1991. MR 92j:35016
6. [B] A. Bahri, The variational contribution of the periodic orbits provided by Birkhoff-Lewis Theorem (with applications to convex Hamiltonians and to three-body type problems), Duke Math. J. 70 (1993), 1-205. MR 94g:58036
7. [FFG] A. T. Fomenko, D. G. Fuchs, V. V. Gutenmacher, Homotopic Topology, Academiai Kiado, Budapest, 1986. MR 88f:55001
8. [G] W. B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc. 204 (1975), 113-135. MR 51:14152
9. [Ha] J. K. Hale, Asymptotic behavior of dissipative systems, Math. Surveys and Monographs, vol. 25, AMS, 1988. MR 89g:58059
10. [Ham] R. Hamilton, Harmonic Maps of Manifolds with Boundary, Lecture Notes in Mathematics, vol. 471, Springer Verlag, 1975. MR 58:2872
11. [H] D. Henry, Geometric Theory of Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, 1981. MR 83j:35084
12. [JM] S. Jimbo and Y. Morita, Stability of nonconstant steady-state solutions to a Ginzburg-Landau equation in higher space dimensions, Nonlinear Anal. TMS 22 (1994), 753-770. CMP 94:10
13. [KW] K. Kishimoto and M. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction diffusion systems on convex domain, J. Differential Equations 58 (1985), 15-21. MR 87a:35105
14. [L] J. L. Lions, Quelques méthodes de résolution des problemes aux limites non lineaires, Dunod, Paris, 1969. MR 41:4326
15. [M] W. S. Massey, Algebraic Topology: An Introduction, Harcourt Brace and World, Inc., New York, 1967. MR 35:2271
16. [N] Y. Nishiura, Coexistence of infinitely many stable solutions to reaction diffusion systems in the singular limit, Dynamics Reported New Series, No. 3 (1994), 25-103.
17. [R] P. M. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184. MR 57:1674
18. [W] G. W. Whitehead, Elements of Homotopy Topology, Springer-Verlag, 1978. MR 80b:55001