Abstract
In this lecture we will examine two different conjectures about the onset of turbulence in dynamical systems that depend on a real parameter. These are the Hopf-Landau (HL) Conjecture and the Ruelle-Takens (RT) Conjecture. We have noticed, in conversations with some experts in dynamical systems, a general attitude that these two conjectures are not only different (which is obvious) but, in fact, incompatible. What we propose to show in this lecture is that there are sound mathematical reasons for concluding that, for a large class of dynamical systems, these conjectures can be compatible. In other words we will show that one can have Hopf-Landau bifurcations in the vicinity of strange attractors.
Supported in part by NSF grant MCS79-01998. Also part of this research was done while author was a Visiting Professor at the University of Southern California.
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Sell, G.R. (1981). Hopf-Landau Bifurcation Near Strange Attractors. In: Haken, H. (eds) Chaos and Order in Nature. Springer Series in Synergetics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68304-6_10
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DOI: https://doi.org/10.1007/978-3-642-68304-6_10
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