Homotopy invariants of time reversible periodic orbits II. Towards applications

Journal of Differential Equations

Volumn 126, Issue 2, 1996, Pages 204-223

  Fiedler, Bernold ^a   Heinze, Steffen ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030577962     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0049     Document Type: Article

References (35)

1. M. ABRAMOWITZ AND I. A. STEGUN (Eds.), "Handbook of Mathematical Functions," Dover, New York, 1965.
2. J. C. ALEXANDER AND J. A. YORKE, Global bifurcation of periodic orbits, Amer. J. Math. 100 (1978), 263-292.
3. P. BRUNOVSKY AND B. FIEDLER, Connecting orbits in scalar reaction diffusion equations, in "Dynamics Reported 1," pp. 57-89, Springer-Verlag, Berlin 1988.
4. S.-N. CHOW, B. DENG, AND B. FIEDLER, Homoclinic bifurcation at resonant eigenvalues, J. Dynamics Diff. Eq. 2 (1990), 177-244.
5. S.-N. CHOW AND J. MALLET-PARET, The Fuller index and global Hopf bifurcation, J. Diff. Eq. 29 (1978), 66-85.
6. S.-N. CHOW, J. MALLET-PARET, AND J. A. YORKE, A periodic orbit index, which is a bifurcation invariant, in "Geometric Dynamics" (J. Palis, Jr., Ed.), Lect. Notes in Math., Vol. 1007, Springer-Verlag, New York 1983.
7. K. DEIMLING, "Nonlinear Functional Analysis," Springer-Verlag, Berlin 1985.
8. R. DEVANEY, Reversible diffeomorphisms and flows, Trans. Amer. Math. Soc. 218 (1976), 89-113.
9. P. G. LEJEUNE-DIRICHLET, "Werke II," G. Reimer, Berlin 1897.
10. I. EKELAND, "Convexity Methods in Hamiltonian Mechanics," Springer-Verlag, Berlin, 1990.
11. I. EKELAND AND H. HOFER, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Invent. Math. 81 (1985), 155-188.
12. B. FIEDLER, An index for global Hopf bifurcation in parabolic systems, J. Reine Angew. Math. 359 (1985), 1-36.
13. B. FIEDLER, "Global Bifurcation of Periodic Solutions with Symmetry," Lect. Notes in Math., Vol. 1309, Springer-Verlag, Berlin/New York, 1988.
14. B. FIEDLER, Global pathfollowing of homoclinic orbits in two-parameter flows, preprint 1992.
15. B. FIEDLER AND S. HEINZE, Homotopy invariants of time reversible periodic orbits I: Theory, J. Diff. Eq. 126 (1996), 184-203.
16. K. GEBA AND W. MARZANTOWICZ, Global bifurcation of periodic solutions, Topol. Meth. in Nonl. Anal. 1 (1993), 67-93.
17. J. IZE, I. MASSABO, AND V. VIGNOLI, Degree theory for equivariant maps, Trans. Amer. Math. Soc. 315 (1989), 433-510.
18. K. KIRCHGÄSSNER, Wave-solutions of reversible systems and applications, J. Diff. Eq. 45 (1982), 113-127.
19. A. LASOTA AND J. A. YORKE, Bounds for periodic solutions of differential equations in Banach spaces, J. Diff. Eq. 10 (1971), 83-91.
20. J. MALLET-PARET AND J. A. YORKE, Snakes: oriented families of periodic orbits, their sources, sinks, and continuation, J. Diff. Eq. 43 (1982), 419-450.
21. K. MEYER, Generic bifurcation of periodic points, Trans. Amer. Math. Soc. 149 (1970), 95-107.
22. A. MIELKE, Essential manifolds for elliptic problems in an infinite strip, J. Diff. Eq. 110 (1994), 332-355.
23. G. POLYA AND G. SZEGO, "Problems and Theorems in Analysis," Springer-Verlag, Berlin, 1976.
24. P. H. RABINOWITZ, Periodic solutions of large norm of Hamiltonian systems, J. Diff. Eq. 50 (1983), 33-48.
25. P. H. RABINOWITZ, "Minimax Methods in Critical Point Theory with Applications to Differential Equations," Memoirs AMS, Vol. 65, Providence, RI, 1986.
26. D. SALAMON AND E. ZEHNDER, Floer homology, the Maslov index, and periodic orbits of Hamiltonian equations, Univ. Warwick, preprint, 1989.
27. R. SCHAAF, "Global Solution Branches of Two Point Boundary Value Problems," Lect. Notes in Math., Vol. 1458, Springer-Verlag, Heidelberg, 1990.
28. M. SEVRUYK, "Reversible Systems," Lect. Notes Math., Vol. 1211, Springer-Verlag, New York, 1986.
29. S. SMALE, Differentiable dynamical systems, Bull. AMS 73 (1967), 747-817.
30. J. SMOLLER, "Shock Waves and Reaction Diffusion Equations," Grundlehren d. Math. Wiss., Vol. 258, Springer-Verlag, New York, 1983.
31. M. STRUWE, "Variational Methods," Springer-Verlag, Berlin, 1990.
32. A. VANDERBAUWHEDE, "Local Bifurcation and Symmetry," Pitman, Boston, 1982.
33. A. VANDERBAUWHEDE, Subharmonic branching in reversible systems, SIAM J. Math. Anal. 21 (1990), 954-979.
34. A. VANDERBAUWHEDE AND B. FIEDLER, Homoclinic period blow-up in reversible and conservative systems, Z. Angew. Math. Phys. 43 (1992), 292-318.
35. Z. ZEHNDER, Periodische Lösungen von Hamiltonschen Systemen, Jahresber. Deutsch. Math.-Verein. 89 (1987), 33-59.