Abstract
Chaos-generating folded 2-dimensional maps can be generalized to higher dimensions in two ways: as folded-towel (or pancake) maps and as bent-walking-stick (or noodle) maps. The noodle case is of mathematical interest because the topologically one-dimensional attractors involved may, despite their thinness, be of the “non-sink” type (that is, stand in a bijective relation to their domain of attraction). Moreover, Shtern recently showed that the well-known Kaplan-Yorke conjecture on the fractal dimensionality of chaotic attractors may fail in the case of noodle maps. We present here an explicit 3-variable noodle map with constant divergence (constant Jacobian determinant). The example is a higher analogue to the Hénon diffeomorphism. A map of similar shape was recently found experimentally by Rob Shaw in a study of the irregularly dripping faucet.
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© 1984 Springer-Verlag Berlin Heidelberg
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Rössler, O.E., Hudson, J.L., Farmer, J.D. (1984). Noodle-Map Chaos: A Simple Example. In: Schuster, P. (eds) Stochastic Phenomena and Chaotic Behaviour in Complex Systems. Springer Series in Synergetics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69591-9_5
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DOI: https://doi.org/10.1007/978-3-642-69591-9_5
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