In this paper we employ the Lyapunov–Schmidt procedure to set up equivariant Hopf bifurcation theory of functional differential equations of mixed type. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction. © 2010 Elsevier Ltd. All rights reserved.

We consider the set PHω(M) of volume preserving partially hyperbolic diffeomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even Bernoulli, for any C2 diffeomorphism in an open and dense subset of PHω(M). This solves a conjecture of Pugh and Shub, in this setting. Mathematics Subject Classification (2000). 37D30.

The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C∗-algebra. We construct nontrivial K-cycles for the cross-product algebra, thereby extending some results of Connes and Sullivan to higher dimensions. We also show how the Patterson-Sullivan measure on the limit set can be interpreted as a center-valued KMS state.

In ancient Mesopotamia, the functions of temple were manifold. It could operate as an administrative center, a center learning, place jurisdiction, for healing, and economic institution, indicated in both textual archaeological sources. All these involved numerous diverse personnel generated interaction with surrounding world, thereby turning into urban life. Because fulfilled all addition to h...

We generalize the Euclidean 1-center approximation algorithm of Bădoiu and Clarkson (2003) to arbitrary Riemannian geometries, and study the corresponding convergence rate. We then show how to instantiate this generic algorithm to two particular settings: (1) the hyperbolic geometry, and (2) the Riemannian manifold of symmetric positive definite matrices.

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By using a Lyapunov function and the center manifold theorem the global stability, the existence of Hopf bifurcation and limit cycles are proved. This result is useful in understanding the nonlinear osci...

As new applications of Schrödinger type inequalities appearing in Jiang (J. Inequal. Appl. 2016:247, 2016), we first investigate the existence and uniqueness of a Schrödingerean equilibrium. Next we propose a tritrophic Hastings-Powell model with two different Schrödingerean time delays. Finally, the stability and direction of the Schrödingerean Hopf bifurcation are also investigated by using t...

We construct an invariant manifold of periodic orbits for a class of non-linear Schrödinger equations. Using standard ideas of the theory of center manifolds, we rederive the results of Soffer and Weinstein ([SW1], [SW2]) on the large time asymptotics of small solutions (scattering theory).

We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of themodel and show the existence ofHopf bifurcation at the positive equilibriumunder some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theo...