Add to ORKGIn this paper several recent results concerning the dynamics of order preserving (sub) homogeneous maps on polyhedral cones are reviewed. These results were obtained by the author in collaboration with Marianne Akian, Stephane Gaubert, Roger Nussbaum, Michael Scheutzow and Colin Sparrow in [2], [13] and [15] and are new nonlinear extensions of the Perron-Frobenius theory
Let X ⊂ Rn be a set whose interior is connected and dense in X, ordered by a closed convex cone K ⊂ ...
Let $X\subset \mathbb{R}^{n}$ be a set whose interior is connected and dense in $X$, ordered by a cl...
AbstractIf X is a real n-dimensional space provided with a subnorm π, then the inequality ξ ⩾ π(x) d...
summary:Maps $f$ defined on the interior of the standard non-negative cone $K$ in ${\mathbb{R}}^N$ w...
We examine the problem of extending, in a natural way, order-preserving maps that are defined on the...
We investigate the iterative behaviour of continuous order preserving subhomogeneous maps $f: K\,{\r...
[[abstract]]A unified treatment is offered to reprove known results on the following four highlights...
AbstractIn this paper we associate to generalized cones of rank k in RN certain convex cones in the ...
In his work on the foundations of geometry, Hilbert observed that a formula which appeared in works ...
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developm...
AbstractThis survey deals with the aspects of archimedian partially ordered finite-dimensional real ...
International audienceWe establish a generalized Perron-Frobenius theorem, based on a combinatorial ...
We consider a generalized notion of differential positivity of a dynamical system with respect to co...
Abstract. When a homogeneous convex cone is given, a natural partial order is introduced in the ambi...
AbstractAn abstract Hardy-Littlewood-Polya type inequality is derived in order to show that the Perr...
Let X ⊂ Rn be a set whose interior is connected and dense in X, ordered by a closed convex cone K ⊂ ...
Let $X\subset \mathbb{R}^{n}$ be a set whose interior is connected and dense in $X$, ordered by a cl...
AbstractIf X is a real n-dimensional space provided with a subnorm π, then the inequality ξ ⩾ π(x) d...
summary:Maps $f$ defined on the interior of the standard non-negative cone $K$ in ${\mathbb{R}}^N$ w...
We examine the problem of extending, in a natural way, order-preserving maps that are defined on the...
We investigate the iterative behaviour of continuous order preserving subhomogeneous maps $f: K\,{\r...
[[abstract]]A unified treatment is offered to reprove known results on the following four highlights...
AbstractIn this paper we associate to generalized cones of rank k in RN certain convex cones in the ...
In his work on the foundations of geometry, Hilbert observed that a formula which appeared in works ...
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developm...
AbstractThis survey deals with the aspects of archimedian partially ordered finite-dimensional real ...
International audienceWe establish a generalized Perron-Frobenius theorem, based on a combinatorial ...
We consider a generalized notion of differential positivity of a dynamical system with respect to co...
Abstract. When a homogeneous convex cone is given, a natural partial order is introduced in the ambi...
AbstractAn abstract Hardy-Littlewood-Polya type inequality is derived in order to show that the Perr...
Let X ⊂ Rn be a set whose interior is connected and dense in X, ordered by a closed convex cone K ⊂ ...
Let $X\subset \mathbb{R}^{n}$ be a set whose interior is connected and dense in $X$, ordered by a cl...
AbstractIf X is a real n-dimensional space provided with a subnorm π, then the inequality ξ ⩾ π(x) d...