Lin's method for discrete dynamical systems

Journal of Difference Equations and Applications

Volumn 6, Issue 5, 2000, Pages 577-623

  Knobloch, J ^a  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Discrete dynamical system; Homoclinic point; Lin's method; Shift dynamics

Indexed keywords

EID: 0242648399     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236190008808247     Document Type: Article

References (13)

1. J. Knobloch, Bifurcation of degenerate homoclinic orbits in reversible and conservative systems, J. Dyn. Diff. Eqns. 9(3), 1997, All-AAA.
2. J. Knobloch, Dynamics near non-transversal homoclinic points (in preparation).
3. J. Knobloch, B. Marx and M. El Morsalani, Characterization of homoclinic points bifurcating from degenerate homoclinic orbits, Preprint No. M 13/97 TU llmenau, 1997.
4. J. Knobloch and B. Sandstede, Lin's method for degenerate homoclinic orbits (in preparation).
5. J. Knobloch and U. Schalk, Homoclinic points near degenerate homoclinics, Nonlinearity 8 (1995), 1133-1141.
6. X.-B. Lin, Using Melnikovs method to solve Shilnikovs problems, Proc. Roy. Soc. Edinburgh 116A (1990), 295-325.
7. K.J. Palmer, Exponential dichotomies, the shadowing lemma and transversal homoclinic points, in: Dynamics Reported, Vol, I, John Wiley & Sons and B.G. Teubner, 1988, pp. 265-306,
8. K.J. Palmer, Exponential Dichotomies and Transversal Homoclinic Points, J. Diff. Eqns. 55(1984), 225-256.
9. B. Sandstede, Verzweigungstheorie homokliner Verdoppelungen, IAAS Report
10. A. Vanderbauwhede, Bifurcation of degenerate homoclinics, Results in Math. 21 (1992), 211-223.
11. A. Vanderbauwhede and B. Fiedler, Homoclinic period blow-up in reversible and conservative systems, ZAMP 43 (1992), 292-318.
12. S, Wiggins, Introduction to Nonlinear Applied Nonlinear Dynamical Systems and Chaos, Springer Verlag, Berlin, 1990.
13. E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. I Fixed Point Theorems. Springer Verlag, Berlin, 1993.