Rössler, O. E. An equation for hyperchaos. (English) Zbl 0996.37502 Phys. Lett., A 71, No. 2-3, 155-157 (1979). The author investigates a four-variable oscillator that contains only one nonlinear quadratic term. By numerical simulation it is shown that the quadratic term produces chaos with two directions of hyperbolic instability on the attractor. He conjectures that in case this result is valid for systems of higher dimension than 4, turbulences may involve more than one direction of lateral instability, so turbulence may be hyperchaos of high order. Cited in 2 ReviewsCited in 318 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior PDF BibTeX XML Cite \textit{O. E. Rössler}, Phys. Lett., A 71, No. 2--3, 155--157 (1979; Zbl 0996.37502) Full Text: DOI References: [1] Rossler, O.E., Z. naturforsch., 31a, 1664, (1976) [2] Rossler, O.E., Ann. NY acad. sci., 316, 376, (1979) [3] Smale, S., Bull. am. math. soc., 73, 747, (1967) [4] Rossler, O.E., Chaotic oscillations - an example of hyperchaos, () · Zbl 0451.58024 [5] Rossler, O.E., Phys. lett., 57A, 397, (1976) [6] Rossler, O.E., Bull. math. biol., 39, 275, (1977) [7] Rossler, O.E., Z. naturforsch., 31a, 259, (1976) [8] O.E. Rossler, I. Gumowski and C. Mira, in preparation. [9] Lorenz, E.N., J. atmos. sci., 20, 130, (1963) [10] Haken, H., Phys. lett., 53A, 77, (1975) [11] Kuramoto, Y.; Yamada, T., Prog. theor. phys., 55, 679, (1976) [12] Rossler, O.E., Z. naturforsch., 31a, 1168, (1976) [13] Rossler, O.E., Chaos, () · Zbl 0372.58012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.