The meromorphic maps fλ(z) = λ(1−exp(−2z))−1, λ > 0, of the complex plane are thoroughly investigated. With each map fλ associated is its projection Fλ on the infinite cylinder Q. This map and the set Jr(Fλ) consisting of those points in the cylinder Q whose ω-limit set under Fλ is not contained in the set {0,−∞} will form the primary objects of our interest in this article. Let hλ = HD(Jr(Fλ))...

We are interested in the statistical behavior of a certain continued fraction whose associated dynamical system has infinite invariant measure. show growth rate denominator $Q_n$ $n$-th convergent negative expansion $x$ and approximation: $$ \frac{\log{n}}{n}\log{\left|x-\frac{P_n}{Q_n}\right|}\rightarrow -\frac{\pi^2}{3} \quad \text{in measure} for $x$. In course proof, we reprove related resu...

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-pr...

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with singlepeaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve effi...

Let X be an infinite compact metric space with finite covering dimension. Let α, β : X → X be two minimal homeomorphisms. Suppose that the range of K0-groups of both crossed product C∗-algebras are dense in the space of real affine continuous functions. We show that α and β are approximately conjugate uniformly in measure if and only if they have affine homeomorphic invariant probability measur...

Let X be an infinite compact metric space with finite covering dimension. Let α, β : X → X be two minimal homeomorphisms. Suppose that the range of K0-groups of both crossed products are dense in the space of real affine continuous functions. We show that α and β are approximately conjugate uniformly in measure if and only if they have affine homeomorphic invariant probability measure spaces.

Consider a complete hyperbolic surface which can be partitioned into countably many pairs of pants whose boundary components have lengths less than some constant. We show that any infinite ergodic invariant Radon measure for the horocycle flow is either supported on a a single horocycle associated with a cusp, or corresponds canonically to an extremal positive eigenfunction of the Laplace–Beltr...

A two-dimensional linear time invariant arises in image processing and geophysics for processing seismic, gravity as well as magnetic data. Two dimensional recursive filters in the frequency domain poses a great challenge in its stability which affects the output that need to be very accurate. Many algebraic schemes are on hand to test the stability of two-dimensional systems. A typical algebra...