The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory. PACS: 03.65.Bz, 03.67.-a, 03.65.Yz

A cycle expansion technique for discrete sums of several PF operators, similar to the one used in the standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particular mappings entering the sum.

This paper presents simple proofs of the principal results of the Perron-Frobenius theory for linear mappings on finite-dimensional spaces which are nonnegative relative to a general partial ordering on the space. The principal tool for these proofs is an application of the theory of norms in finite dimensions to the study of order inequalities of the form Ax S ax, x è 0 where A ^ 0. This appro...

Exotic semirings such as the “(max;+) semiring” (R[f 1g;max;+), or the “tropical semiring” (N[f+1g;min;+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, Hamilton-Jacobi theory; asymptotic analysis (lo...

We advance support variety theory for finite tensor categories. First we show that the dimension of an object equals rate growth a minimal projective resolution as measured by Frobenius-Perron dimension. Then every conical subvariety unit may be realized object. Finally, indecomposable is connected.

We present a dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in literature. As result, we develop complex version of prove generalized Krein-Rutman type theorems.

We present a new approach of proving certain Carath\'{e}odory-type theorems using the Perron-Frobenius Theorem, classical result in matrix theory describing largest eigenvalue with positive entries. One problems left open this note is whether our may be extended to prove similar results area, particular Colourful Carath\'{e}odory Theorem.