Hidden dynamics for piecewise smooth maps. (English) Zbl 1473.37046
This paper is devoted to the regularization of piecewise smooth systems by constructing continuous approximations to them. The authors introduce a hidden dynamics approach to piecewise smooth one-dimensional maps motivated by the results of the second author and S. Webber [Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190473, 19 p. (2020; Zbl 1439.37051)]. In their method, it is necessary to blow up the discontinuity and all its preimages into intervals, which is a similar construction to the Denjoy circle map counterexample.
Reviewer: Steve Pederson (Atlanta)
MSC:
| 37E05 | Dynamical systems involving maps of the interval |
| 37E10 | Dynamical systems involving maps of the circle |
Citations:
Zbl 1439.37051References:
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