Time-scaling symmetry and Zeno solutions

J.M. Schumacher

Research output: Contribution to journalArticleScientificpeer-review

18 Citations (Scopus)


Symmetries are often helpful in reducing the complexity of the analysis of dynamical systems. Here we discuss a symmetry that combines a transformation in space with a scaling of time. Examples are given of a number of nonsmooth dynamical systems in which a symmetry of this type occurs. The time-scaling symmetry can be combined with return mapping analysis to achieve a dimension reduction in addition to the one already obtained from considering the return map. The method is applied in a study of Zeno behavior in linear systems with relay feedback.
Original languageEnglish
Pages (from-to)1237-1242
Issue number5
Publication statusPublished - 2009


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