TY - JOUR
T1 - Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps
AU - Gardini, Laura
AU - Tramontana, Fabio
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Circle map
KW - Piecewise-linear map
KW - Circle map
KW - Piecewise-linear map
UR - http://hdl.handle.net/10807/67462
U2 - 10.1016/j.chaos.2012.07.007
DO - 10.1016/j.chaos.2012.07.007
M3 - Article
SN - 1873-2887
VL - 45
SP - 1328
EP - 1342
JO - CHAOS, SOLITONS & FRACTALS
JF - CHAOS, SOLITONS & FRACTALS
ER -