Abstract We give a setting of the Diaconis–Freedman chain in multi-dimensional simplex and consider its asymptotic behavior. By using techniques from random iterated function theory quasi-compact operator theory, we first some sufficient conditions which ensure existence uniqueness an invariant probability measure and, particular cases, explicit formulas for density. Moreover, completely classi...

In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra quasilocal algebra. We show that algebras coarse invariants, hence encoding geometric information underlying spaces. prove geometry which admits embedding into Hilbert space, inclusion induces an isomorphism in $K$-theory.

this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...