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Discretizing the fold bifurcation - a conjugacy result. (English) Zbl 1174.37013

Summary: In the vicinity of fold bifurcation points, the time-\(h\) exact and the stepsize-\(h\) discretized dynamics are shown to be equivalent via a two-parameter family of conjugacies. The problem of optimal conjugacy estimates remains open.

MSC:

37G10 Bifurcations of singular points in dynamical systems
34C23 Bifurcation theory for ordinary differential equations
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
65L70 Error bounds for numerical methods for ordinary differential equations
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