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Bifurcation of homoclinic structures. II: The asymptotic fate of periodic points, collocation and finite element approximation. (English) Zbl 0886.58086

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.

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

Citations:

Zbl 0886.58085
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