Transversality of homoclinic orbits and exponential dichotomies for parabolic equations

Journal of Mathematical Analysis and Applications

Volumn 216, Issue 2, 1997, Pages 466-480

  Weiyao, Zeng ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

EXPONENTIAL DICHOTOMY; LINEAR PARABOLIC EQUATION; MELNIKOV METHOD; TRANSVERSAL HOMOCLINIC ORBIT;

DIFFERENTIAL EQUATIONS;

EID: 0031574597     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5662     Document Type: Article

References (23)

1. Palmer K. J. Exponential dichotomies and transversal homoclinic points. J. Differential Equations. 55:1984;225-256.
2. Meyer K. R., Sell G. R. Melnikov transforms, Bernoulli bundles and almost periodic perturbations. Trans. Amer. Math. Soc. 314:1989;63-105.
3. Meyer K. R., Sell G. R. An analytic proof of the shadowing lemma. Funkcial. Ekvac. 30:1987;127-133.
4. Hale J. K., Lin X. B. Exponential dichotomies and homoclinic orbits in functional differential equations. J. Differential Equations. 63:1986;227-254.
5. Coppel W. A. Dichotomies in Stability Theory. 1978;Springer-Verlag, New York.
6. Weiyao Z. Exponential dichotomies and transversal homoclinic orbits in degenerate cases. J. Dynamics Differential Equations. 7:1995.
7. Blazquez C. Miguel. Transverse homoclinic orbits in periodically perturbed parabolic equations. Nonlinear Anal. 10:1986;1277-1291.
8. Melnikov V. K. On the stability of the center for time-periodic perturbations. Trans. Moscow Math. Soc. 12:1964;1-57.
9. Wiggins S. Global Bifurcations and Chaos. Appl. Math. Sci. 73:1988;Springer-Verlag, New York.
10. Hale J. K., Chow S. N. Methods of Bifurcations. 1982;Springer-Verlag, New York/Berlin.
11. Palmer K. J. Transversal heteroclinic orbits and Cherry's example of a non-integrable Hamiltonian systems. J. Differential Equations. 65:1986;321-360.
12. Chow S. N., Hale J. K., Mallet-Paret J. An example of bifurcation to homoclinic orbits. J. Differential Equations. 37:1980;351-373.
13. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lectures Notes in Mathematics. 840:1981;Springer-Verlag, New York/Berlin.
14. Weinian Z. The Fredholm alternative and exponential dichotomies for parabolic equations. J. Math. Anal. Appl. 191:1995;180-201.
15. Battelli F. Heteroclinic orbits in singular systems: A unifying approach. J. Dynamics Differential Equations. 6:1994;147-173.
16. Sacker R. J., Sell G. R. Dichotomies for linear evolutionary equations in Banach spaces. J. Differential Equations. 113:1994;17-67.
17. Chow S. N., Leiva H. Existence and roughness of the exponential dichotomies for skew-product semiflow in Banach spaces. J. Differential Equations. 120:1995;429-477.
18. B. Sandstede, 1993, Verzweigungstheorie homokliner Verdopplungen, University of Stuttgart.
19. Sacker R. J., Sell G. R. Existence of dichotomies and invariant splittings for linear systems, I. J. Differential Equations. 15:1974;429-458.
20. Shen W., Yi Y. Asymptotic almost periodicity of scalar parabolic equations with almost periodic time dependence. J. Differential Equations. 122:1979;373-379.
21. Shen W., Yi Y. On minimal sets of scalar parabolic equations with skew-product structures. Trans. Amer. Math. Soc. 347:1995;4413-4431.
22. Hale J. K., Magalhaes L. T., Oliva W. M. An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory. 1984;Springer-Verlag, New York/Berlin.
23. Fiedler B., Rocha C. Heteroclinic orbits of semilinear parabolic equations. J. Differential Equations. 125:1996;239-281.