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.

Gardini, L., Tramontana, F., Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps, <<CHAOS, SOLITONS & FRACTALS>>, 2012; 45 (11): 1328-1342. [doi:10.1016/j.chaos.2012.07.007] [http://hdl.handle.net/10807/67462]

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

Tramontana, Fabio
2012

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.
Inglese
Gardini, L., Tramontana, F., Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps, <<CHAOS, SOLITONS & FRACTALS>>, 2012; 45 (11): 1328-1342. [doi:10.1016/j.chaos.2012.07.007] [http://hdl.handle.net/10807/67462]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/67462
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