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On some properties of focal points. (English) Zbl 1196.54070
In continuation to their work [Discrete Dyn. Nat. Soc. 2005, No. 3, 343–355 (2005; Zbl 1137.37021)], the authors study dynamical properties of two dimensional maps having an inverse with vanishing denominator. A prefocal curve of a map is a set of points whose image by one inverse is reduced into a single point called a focal point. The authors discuss facts regarding the role of focal points and prefocal curves. Further, they investigate necessary and/or sufficient conditions for a focal point to be a fixed point of the inverse map. Finally, applications are discssed by considering two examples with one focal point and two focal points.
MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
47H10 Fixed-point theorems
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References:
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