Stationary states for discrete dynamical systems in the plane. (English) Zbl 1011.37021
Summary: The existence of a fixed point for maps of the form \(\text{Identity}+ \text{Contraction}\) acting on \(\mathbb{R}^2\) is established under quite general conditions. A counterexample is given in \(\mathbb{R}^3\).
MSC:
| 37E05 | Dynamical systems involving maps of the interval |
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
| 39A12 | Discrete version of topics in analysis |
