The use of subhomogeneous monotone maps in multiplicative and additive nonlinear Perron-Frobenius theory

An overview of results on the properties of orbits of some classes of order-preserving nonlinear dynamical systems in Banach spaces is provided. The article focuses on discrete dynamical systems generated by the so-called subhomogeneous mappings. The nonlinear generalizations of the theorem of Perron-Frobenius for various classes of monotone maps are analyzed.