Gerling, Jürgen; Jürgens, Hartmut; Peitgen, Heinz-Otto Bifurcation of homoclinic structures. II: The asymptotic fate of periodic points, collocation and finite element approximation. (English) Zbl 0886.58086 Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, No. 3, 527-549 (1997). Summary: This paper is a continuation of the authors’ part I [ibid., No. 2, 287-317 (1997; see the review above)] and investigates the periodic structure of a specific area-preserving homeomorphism which is generated by the finite difference approximation for a nonlinear boundary value problem. Moreover, these and prior results are extended to further approximation schemes like collocation and finite elements. Cited in 1 Review MSC: 37G99 Local and nonlocal bifurcation theory for dynamical systems 34C23 Bifurcation theory for ordinary differential equations 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations Keywords:bifurcation; periodic structure; area-preserving homeomorphism; nonlinear boundary value problem Citations:Zbl 0886.58085 PDFBibTeX XMLCite \textit{J. Gerling} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, No. 3, 527--549 (1997; Zbl 0886.58086) Full Text: DOI