The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable
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In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow defined on the unit disk, outputs the exact number of the (hyperbolic) equilibrium points as well the locations of all equilibriums with arbitrary precision. By arbitrary accuracy it is meant that the accuracy is included in the input of the algorithm. As a consequence, we obtain a root-finding algorithm that computes the set of all zeros of a continuously differentiable function f defined on the unit ball of ℝ^d with arbitrary accuracy, provided that the Jacobian of f is invertible at each zero of f; moreover, the computation is uniform in f.
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