Finite-dimensional right ideals in some algebras associated with a locally compact group

Let be a discrete group, a commutative discrete cancellative semigroup or a locally compact abelian group. Let be the space of bounded, uniformly continuous, complex-valued functions on With an Arens-type product, the conjugate becomes a Banach algebra. We prove, that unlike left ideals, finite-dimensional right ideals exist in if and only if is compact.

     

Irregular cusps of ball quotients

We study the branch divisors on the boundary of the canonical toroidal compactification of ball quotients. We show a criterion, the low slope cusp form trick, for proving that ball quotients are of general type. Moreover, we classify when irregular cusps exist in the case of the discriminant kernel and construct concrete examples for some arithmetic subgroups. As another direction of study, when a complex ball is embedded into a Hermitian symmetric domain of type IV, we determine when regular or irregular cusps map to regular or irregular cusps studied by Ma.     

Zero-Hopf Bifurcation at the Origin and Infinity for a Class of Generalized Lorenz System

In this paper, the zero-Hopf bifurcations are studied for a generalized Lorenz system. Firstly, by using the averaging theory and normal form theory, we provide sufficient conditions for the existence of small amplitude periodic solutions that bifurcate from zero-Hopf equilibria under appropriate parameter perturbations. Secondly, based on the Poincar{\''e} compactification, the dynamic behavior of the generalized Lorenz system at infinity is described, and the zero-Hopf bifurcation at infinity is investigated. Additionally, for the above theoretical results, some related illustrations are given by means of the numerical simulation.