Non-strange chaotic attractors equivalent to their templates

Abstract

We construct systems of three autonomous first-order differential equations with bounded two-dimensional attracting sets M. The semi-flows on M are chaotic and have one-dimensional Poincaré sections whose Poincaré maps project to chaotic maps of the interval. The attractors are two-dimensional rather than fractal, and when ‘unzipped’ they are topologically equivalent to the templates of suspended horseshoes.

Keywords:

• attractor
• template
• chaos

Acknowledgements

The author thanks the reviewers for helpful comments that improved this article, and for pointing out relevant work by S.P. Kuznetsov on hyperbolic flows.