Polynomial estimates and discrete saddle-node homoclinic orbits

Journal of Mathematical Analysis and Applications

Volumn 256, Issue 1, 2001, Pages 115-126

  Hüls, Thorsten ^a   Zou, Yongkui ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b JILIN UNIVERSITY   (China)

Author keywords

Polynomial rate of convergence; saddle node homoclinic orbit; center manifold

Indexed keywords

EID: 0035315309     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7294     Document Type: Article

References (15)

1. Arnol'd V., Afraimovich V., Il'yashenko Y., Shil'nikov L. Bifurcation theory. Arnol'd V. Dynamical Systems. V. Encyclopaedia of Mathematical Sciences. 1994;Springer-Verlag, New York.
2. Beyn W.-J. On well-posed problems for connecting orbits in dynamical systems. Contemp. Math. 172:1994;131-168.
3. Chow S.-N., Lin X.-B. Bifurcation of a homoclinic orbit with a saddle-node equilibrium. Differential Integral Equations. 3:1990;435-466.
4. Coddington E. A., Levinson N. Theory of Ordinary Differential Equations. 1955;McGraw-Hill, New York.
5. Coppel W. A. Dichotomies in Stability Theory. Lecture Notes in Mathematics. 629:1978;Springer-Verlag, New York.
6. Fenichel N. Asymptotic stability with rate conditions. Indiana Univ. Math. J. 23:1974;1109-1137.
7. Hartman P. Ordinary Differential Equations. 1964;Wiley, New York.
8. Hirsch M. W., Pugh C. C., Shub M. Invariant Manifolds. Lecture Notes in Mathematics. 583:1977;Springer-Verlag, New York.
9. Ilyashenko Y., Li W. Nonlocal Bifurcations. Mathematical Surveys and Monographs. 66:1999;Amer. Math. Society, Providence.
10. Iooss G. Bifurcation of Maps and Applications. 1979;North-Holland, Amsterdam.
11. Kuznetsov Y. A. Elements of Applied Bifurcation Theory. Applied Mathematical Sciences. 112:1998;Springer-Verlag, New York.
12. Palmer K. J. Exponential dichotomies, the shadowing lemma and transversal homoclinic points. Kirchgraber U., Walther H. O. Dynamics Reported. 1988;265-306 Teubner, Stuttgart.
13. Rainville E. D. Special Functions. 1971;Chelsea, New York.
14. Schecter S. Numerical computation of saddle-node homoclinic bifurcation points. SIAM J. Numer. Anal. 30:1993;1155-1178.
15. Takens F. Partially hyperbolic fixed points. Topology. 10:1971;133-147.