Since there are chaotic nonstrange attractor (CNA) and strange nonchaotic attractor (SNA), are there corresponding chaotic nonstrange saddle (CNS) or strange nonchaotic saddle (SNS)? Although the chaotic saddles in the meaning of Smale horseshoe are always fractal (Cantor Set) thus strange.
chaotic saddle; chaos; strange (fractal)
I think so at least for strange nonchaotic saddles. Saddles are created by intersections between stable and unstable manifolds which may have fractal structures. However, the created saddles may still have periodic structures composed of several subsets of points on certain Poincare section. Within each such subset of points it has fractal structures but between those subsets, the order of iteration under the related Poincare map is determined rather than chaotic.
Dear Thilo Gross, thank you for your attention. You mentioned that an unstable manifold is added so that a strange non-chaotic attractor will be a saddle. However, this is what I am curious that if the non-chaotic property will hold under this transition.
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