Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones

作者：

Highlights：

• Trapping regions and invariant expanding cones are constructed for planar piecewise-linear maps.

• Induced maps are used to accommodate dynamics with rotational characteristics.

• Chaos is verified by proving positivity of a Lyapunov exponent.

• These properties are formulated as an algorithm for establishing the presence of a chaotic attractor.

摘要

•Trapping regions and invariant expanding cones are constructed for planar piecewise-linear maps.•Induced maps are used to accommodate dynamics with rotational characteristics.•Chaos is verified by proving positivity of a Lyapunov exponent.•These properties are formulated as an algorithm for establishing the presence of a chaotic attractor.

论文关键词：Robust chaos,Induced maps,Piecewise-linear systems,Piecewise-smooth systems,Hybrid systems

论文评审过程：Received 12 August 2021, Revised 6 April 2022, Accepted 24 June 2022, Available online 6 August 2022, Version of Record 6 August 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127357