We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these innnite dimensional dynamical systems which exhibits space-time-chaos.

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...

We introduce a relative notion of the ’big images and preimages’-property for random topological Markov chains. This then implies that a relative version of the Ruelle-Perron-Frobenius theorem holds with respect to summable and locally Hölder continuous potentials.

We study the Perron-Frobenius operator P of closed dynamical systems and certain open dynamical systems. We prove that the presence of a large positive eigenvalue ρ of P guarantees the existence of a 2-partition of the phase space for which the escape rates of the open systems defined on the two partition sets are both slower than − log ρ. The open systems with slow escape rates are easily iden...

This paper presents an analytical model for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalu...