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arXiv · 1910.03361

Topological properties of Lorenz maps derived from unimodal maps

Ana Anušić·Henk Bruin·Jernej Činč
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Abstract

A symmetric Lorenz map is obtain by ``flipping'' one of the two branches of a symmetric unimodal map. We use this to derive a Sharkovsky-like theorem for symmetric Lorenz maps, and also to find cases where the unimodal map restricted to the critical omega-limit set is conjugate to a Sturmian shift. This has connections with properties of unimodal inverse limit spaces embedded as attractors of some planar homeomorphisms.

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Ana Anušić, Henk Bruin, Jernej Činč. 2019-10-08. Topological properties of Lorenz maps derived from unimodal maps. https://arxiv.org/abs/1910.03361

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