Monotone maps, the likeness relation and G-structures

Monotone Functions and Maps

In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...

Monotone Maps: a review

The aim of this paper is to provide a brief review of the main results in the theory of discrete-time monotone dynamics.

Generalized Monotone Nonsmooth Maps

Recent characterizations of various types of differentiable generalized monotone maps by Karamardian– Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplis...

Collapsing along monotone poset maps

For a poset P we let Δ(P) denote its nerve: the simplicial complex whose simplices are all chains of P. For a simplicial complex X we let V(X) denote the set of its vertices. An elementary collapse in a simplicial complex X is a removal of two open simplices σ and τ from X , such that dimσ = dimτ +1, and σ is the only simplex of X , different from τ itself, which contains the simplex τ in its c...

Random Iterates of Monotone Maps