Abstract
The Srzednicki method of periodic segments has proven to be a very powerful in detecting chaotic dynamics generated by the periodic in time ODEs. The aim of this note is to introduce the notion of a nested set of periodic segments. We prove a fixed point index formula related to that special configuration of periodic segments. As a consequence, we obtain some results concerning chaotic dynamics. We also provide the examples of periodic planar system with chaotic dynamics emerging from a nested set of periodic segments.
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