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On period-adding sequences of attracting cycles in piecewise linear maps. (English) Zbl 0934.37034

Summary: The authors study numerically bifurcations in a family of bimodal three-piecewise linear continuous one-dimensional maps. Attention is paid to the attracting cycles arising after the bifurcation ‘from unimodal map to bimodal map’. It is found that this type of bifurcation is accompanied by the appearance of period-adding cascades of attracting cycles \(\gamma_{(a_{11}+ a_{12}k)/ (a_{21}+ a_{22}k)}\) which are characterized by \(\rho_k= (a_{11}+ a_{12}k)/ (a_{21}+ a_{22}k)\), \(k= 0,1,\dots\).

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37E05 Dynamical systems involving maps of the interval
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References:

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