Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps

Laura Gardini () and Fabio Tramontana

Chaos, Solitons & Fractals, 2012, vol. 45, issue 11, 1328-1342

Abstract: In this work we consider a simple system of piecewise linear discontinuous 1D map with two discontinuity points: X′=aXif ∣X∣z, where a and b can take any real value,and may have several applications. We show that its dynamic behaviors are those of a linear rotation:either periodic or quasiperiodic, and always structurally unstable. A generalization to piecewise monotone functions X′=F(X) if ∣X∣z is also given, proving the conditions leading to a homeomorphism of the circle.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:11:p:1328-1342

DOI: 10.1016/j.chaos.2012.07.007

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