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Positive Lyapunov exponents for Lorenz-like families with criticalities. (English) Zbl 0944.37025
Flexor, Marguerite (ed.) et al., Géométrie complexe et systèmes dynamiques. Colloque en l’honneur d’Adrien Douady à l’occasion du soixantième anniversaire, Orsay, France, du 3 au 8 juillet 1995. Paris: Astérisque, Astérisque. 261, 201-237 (2000).
Summary: We introduce a class of one-parameter families of real maps extending the classical geometric Lorenz models. These families combine singular dynamics (discontinuities with infinite derivative) with critical dynamics (critical points) and are based on the behaviour displayed by Lorenz flows over a fairly wide range of parameters. Our main result states that – nonuniform – expansion is the prevalent form of dynamics even after the formation of the criticalities.
For the entire collection see [Zbl 0932.00046].

MSC:
37E35 Flows on surfaces
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
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