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From wild Lorenz-like to wild Rovella-like dynamics

机译:从狂野的洛伦兹到狂野的罗维拉

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摘要

We consider a two-dimensional noninvertible map that was introduced by Bamon, Kiwi and Rivera-Letelier as a model of a wild Lorenz-like attractor in a vector field of dimension at least five; such an attractor contains an expanding equilibrium and a hyperbolic set with robust homoclinic tangencies. Advanced numerical techniques enable us to study how the stable, unstable and critical sets of the map change within the conjectured region of wild chaos in the transition from Lorenz-like to Rovella-like dynamics, that is, when the equilibrium of the vector field becomes contracting. We find numerical evidence for the existence of wild Rovella-like attractors, wild Rovella-like saddles and regions of multistability, where a Rovella-like attractor coexists with two fixed-point attractors. We identify bifurcations generating these different types of dynamics and compute them in two-parameter bifurcation diagrams.
机译:我们考虑由Bamon,Kiwi和Rivera-Letelier引入的二维不可逆图,该二维图是在至少5维矢量场中的野生Lorenz样吸引子的模型。这样的吸引子包含一个扩展的平衡和一个具有强大的同宿切线的双曲集。先进的数值技术使我们能够研究在从Lorenz式到Rovella式动力学的过渡(即矢量场的平衡变为)时,在野生混沌的猜想区域内图的稳定,不稳定和临界集如何变化。承包。我们找到了存在像野生Rovella一样的吸引子,像野生Rovella一样的鞍形和多重稳定性区域的数字证据,其中一个Rovella像吸引子与两个定点吸引子共存。我们确定产生这些不同类型动力学的分叉,并在两参数分叉图中进行计算。

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