Bifurcation Patterns in Homogeneous Area-Preserving Piecewise-Linear Maps

• Garcia-Morato, Luis Benadero ^[1] ; Emilio Freire Macias ^[2] ; Enrique Ponce Nuñez ^[2] ; Francisco Torres Peral ^[2]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  2. [2] Universidad Sevilla
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 547-582
• Idioma: inglés
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• Resumen

  • 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.