Using ergodic theory, in this paper we present a Gel’fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup S restricted to a subset that need not carry the algebraic structure of S. This generalizes the Berger-Wang formula. Using it as a tool, we study the absolute exponential stability of ...

Golsar is located in north-west of Rasht the capital city of Guilan province. This region, according to standards 2800, is identified among the regions with relatively high risk of earthquake. A set of historical and instrumental seismicity data used in radius of 200 km which covers the period twelveth century until now. Kijko method has been applied for estimating for parameters considering of...

A pseudo-Anosov surface automorphism φ has associated to it an algebraic unit λφ called the dilatation of φ. It is known that in many cases λφ appears as the spectral radius of a Perron–Frobenius matrix preserving a symplectic form L. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit λ appears as an eigenvalue for some integra...