Two rational numbers are associated to each periodic orbit of Smale's horseshoe, and practical algorithms are given for their calculation. Using these quantities, it is possible to decide in many cases whether or not a given orbit must always be created after some other given orbit in any two-dimensional transition to chaos. A statement of ``weak universality'' for the bifurcation sequence as a whole is formulated.
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Toby Hall (1993) studied this question.
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