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arXiv · 2302.02098

An example derived from Lorenz attractor

Ming Li·Fan Yang·Jiagang Yang·Rusong Zheng
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Abstract

We consider a DA-type surgery of the famous Lorenz attractor in dimension 4. This kind of surgeries have been firstly used by Smale [S] and Ma\~n\'e [M1] to give important examples in the study of partially hyperbolic systems. Our construction gives the first example of a singular chain recurrence class which is Lyapunov stable, away from homoclinic tangencies and exhibits robustly heterodimensional cycles. Moreover, the chain recurrence class has the following interesting property: there exists robustly a 2-dimensional sectionally expanding subbundle (containing the flow direction) of the tangent bundle such that it is properly included in a subbundle of the finest dominated splitting for the tangent flow.

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Ming Li, Fan Yang, Jiagang Yang, Rusong Zheng. 2023-02-04. An example derived from Lorenz attractor. https://arxiv.org/abs/2302.02098

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