Bifurcation patterns in homogeneous area-preserving piecewise-linear maps
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The dynamical behavior of a family of planar continuous piecewise linear maps with two zones is analyzed. Assuming homogeneity and preservation of areas we obtain a canonical form with only two parameters: the traces of the two matrices defining the map. It is shown the existence of sausage-like structures made by lobes linked at the nodes of a nonuniform grid in the parameter plane. In each one of these structures, called resonance regions, the rotation number of the associated circle map is a given rational number. The boundary of the lobes and a significant inner partition line are studied with the help of some Fibonacci polynomials.
CitationBenadero, L., Freire, E., Ponce, E., Torres, F. Bifurcation patterns in homogeneous area-preserving piecewise-linear maps. "Qualitative theory of dynamical systems", August 2019, Vol. 18, issue 2, pp 547-582.