Abstract
In earlier work we defined a computational saddle transition problem which arises in the dynamics of certain hyperbolic toral automorphisms, and proved, using the shadowing lemma, that in an appropriate model of computation this problem is in Oracle NP, up to a highly restricted oracle. In this note we show similar methods can be extended to a far larger class of dynamical systems, a class which is dense in the C0-topology on Diff1(T2). We adapt the fitted diffeomorphisms of Shub and Sullivan on the 2-Torus to a computational framework. Just as in their case, the resulting “well-fitted” toral automorphisms are structurally stable, and C0-dense, and we show the associated saddle transition problems are, in our model, in Oracle NP.
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