Bifurcation Patterns in Homogeneous Area-Preserving Piecewise-Linear Maps

被引：6

作者：

Benadero Garcia-Morato, Luis ^{[1
]}

Freire Macias, Emilio ^{[2
]}

Ponce Nunez, Enrique ^{[2
]}

Torres Peral, Francisco ^{[3
]}

机构：

[1] Univ Politecn Cataluna, ETSETB, Dept Fis Aplicada, Jordi Girona1, Barcelona 08034, Spain

[2] Univ Seville, Escuela Tecn Super Ingn, Dept Matemat Aplicada 2, Seville 41092, Spain

[3] Univ Seville, Escuela Politecn Super, Dept Matemat Aplicada 2, Virgen Africa 7, Seville 41011, Spain

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2019年 / 18卷 / 02期

关键词：

Piecewise linear maps; Bifurcations; Area preserving maps; BORDER-COLLISION BIFURCATIONS; SMOOTH; TONGUES;

D O I：

10.1007/s12346-018-0299-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：547 / 582

页数：36

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