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

Fabio Tramontana, Laura Gardini

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2 Citazioni (Scopus)

Abstract

In this work we consider a simple system of piecewise linear discontinuous 1D map with two discontinuity points: X′ = aX if ∣X∣ < z, X′ = bX if ∣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, X′ = G(X) if ∣X∣ > z is also given, proving the conditions leading to a homeomorphism of the circle.
Lingua originaleEnglish
pagine (da-a)1328-1342
Numero di pagine15
RivistaCHAOS, SOLITONS &amp; FRACTALS
Volume45
DOI
Stato di pubblicazionePubblicato - 2012

Keywords

  • Circle map
  • Piecewise-linear map

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