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 -