Minimal sets of antitriangular maps. Dynamical systems and functional equations (Murcia, 2000). (English) Zbl 1056.37005
Summary: We consider the class of two-dimensional maps \(F(x,y) = (g(y),f(x)), (x,y) \in [0,1] \times [0,1] = I^2\), where \(f\) and \(g\) are continuous interval maps. The paper deals with the structure of minimal sets for this class of maps. We give a complete description of finite minimal sets and prove some partial results concerning the infinite case.
MSC:
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 37E05 | Dynamical systems involving maps of the interval |
| 37E99 | Low-dimensional dynamical systems |
Keywords:
Minimal set; \(\omega\)-limit set; Cantor set; periodic orbit; antitriangular map; topological dynamicsReferences:
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