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1-manifold algebra algorithm applications approximation artificial bifurcation assume asymptotic asymptotic stability Axiom Banach space Bonn bounded set Brouwer degree codimension compact completely labeled simplices computation condition consider constant Continuation Method continuous functions continuous map convergence convex curve defined definition delay equations denote dimension eigenvalues equivalent example figure fixed point index fixed point theorem Fredholm Fredholm operator functional differential equations given global bifurcation Hale hamiltonian path hence homeomorphic homotopy hypothesis implies inequality integer-L-labeling integral Lemma Let f map f Math Mathematical monotonic n-simplex neighborhood nonlinear numerical obtain operator ordinary differential equations oscillating periodic solution oscillating solutions parameter Peitgen periodic solutions perturbation piecewise linear positive problems properties prove regular value resp Saigal satisfies semigroup slowly oscillating periodic solving Sperner simplex stability subset Suppose T-periodic theory topological triangulation unique vector vector-labeling vertex Yorke zero