infinite period bifurcation and global bifurcation branches branches of periodic solutions which exhibit the alternatives of the global hopf bifurcation theorem are calculated for two general systems of differential equations in the first a branch of solu

harmonic functions on hypergroups abstract we initiate a study of harmonic functions on hypergroups in particular we introduce the concept of a nilpotent hypergroup and show such hypergroup admits an invariant measure as well as a liouville theorem for bounded harmonic functions further positive harmonic functions on nilpotent hypergroups are shown to be integrals of exponential functions for arbitrary hypergroups we derive a harnack inequality for positive harmonic functions and prove a liouville theorem for compact hypergroups we discuss an application to harmonic spherical functions

dynamic stability of rotating blades beams eccentrically clamped to a shaft with fluctuating speed abstract in plane bending vibrations of a beam rotating with a periodically fluctuating speed are considered the partial differential equation of motion is discretisized via galerkin s method and a set of mathieu hill equations is obtained the constant speed rotation problem is reviewed and its reflections onto the fluctuating speed problem are underlined dynamic stability analysis is performed via a monodromy matrix method and a generalized bolotin method examples of stability charts are worked out reflecting stability s dependence on various pairs of system parameters

vibration and buckling of flexible rotating beams perturbation techniques are employed to estimate the free vibration characteristics and buckling limit of a flexible rotating bernoulli euler beam the normalized beam stiffness e ei m 2 r 4 is introduced and treated as a small parameter then singular perturbation solutions to the governing eigenvalue problem are derived that are valid up to and including order e for any given hub radius the special case of a zero hub radius is then considered and the corresponding solutions are presented next a transformation is introduced which leads to a regular perturbation formulation of the problem the solution of which is presented the natural frequency mode shape predictions and buckling limits obtained from both the singular and regular perturbation formulations are compared with exact values obtained from a power series solution of the eigenvalue problem the singular perturbation solution matches well with the exact values for small stiffnesses whereas the regular perturbation solution provides an excellent accuracy for all beam stiffnesses and hub radii considered

fixed point properties of semigroups of non expansive mappings abstract in recent years there have been considerable interests in the study of when a closed convex subset k of a banach space has the fixed point property i e whenever t is a non expansive mapping from k into k then k contains a fixed point for t in this paper we shall study fixed point properties of semigroups of non expansive mappings on weakly compact convex subsets of a banach space or more generally a locally convex space by considering the classes of bicyclic semigroups we answer two open questions one posted earlier by the first author in 1976 dalhousie and the other posted by t mitchell in 1984 virginia we also provide a characterization for the existence of a left invariant mean on the space of weakly almost periodic functions on separable semitopological semigroups in terms of fixed point property for non expansive mappings related to another open problem raised by the first author in 1976

bi instability and the global role of unstable resonant orbits in a driven laser driven class b lasers are devices which possess quadratic nonlinearities and are known to exhibit chaotic behavior we describe the onset of global heteroclinic connections which give rise to chaotic saddles these form the precursor topology which creates both localized homoclinic chaos as well as global mixed mode heteroclinic chaos to locate the relevant periodic orbits creating the precursor topology approximate maps are derived using matched asymptotic expansions and subharmonic melnikov theory locating the relevant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser 2000 published by elsevier science b v

jordan structures in harmonic functions and fourier algebras on homogeneous spaces we study the jordan structures and geometry of bounded matrix valued harmonic functions on a homogeneous space and their analogue the harmonic functionals in the setting of fourier algebras of homogeneous spaces

fixed point properties for semigroups of nonlinear mappings and amenability abstract in this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a banach space we also study a schauder fixed point property for a semitopological semigroup of continuous mappings on a compact convex subset of a separated locally convex space such semigroups properly include the class of extremely left amenable semitopological semigroups the free commutative semigroup on one generator and the bicyclic semigroup s 1 a b a b 1

subharmonic hysteresis and period doubling bifurcations for a periodically driven laser the authors consider the laser rate equations for a periodically modulated class b laser the bifurcation diagram of the periodic solutions is analyzed both numerically and theoretically the bifurcation parameter is the amplitude of the periodic modulations concentration is on the period 1 and period 2 branches of solutions that emerge either from a limit point or from a period doubling bifurcation point the bifurcation diagrams of the driven laser are analyzed with and without dissipation it is seen that the laser oscillations become pulsating as their amplitude increases suggesting a new asymptotic analysis ofthe laser oscillations a large parameter proportional to the amplitude of the oscillations is identified andperiodic solutions using singular perturbation techniques are constructed equations for a poincare map are derived and an analytical expression of the first period doubling bifurcation is obtained

negative coupling resonances in pump coupled lasers we consider coupled lasers where the intensity deviations from the steady state modulate the pump of the other lasers most of our results are for two lasers where the coupling constants are of opposite sign this leads to a hopf bifurcation to periodic output for weak coupling as the magnitude of the coupling constants is increased negatively we observe novel amplitude effects such as a weak coupling resonance peak and strong coupling subharmonic resonances and chaos in the weak coupling regime the output is predicted by a set of slow evolution amplitude equations pulsating solutions in the strong coupling limit are described by a discrete map derived from the original model

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

finite dimensional invariant subspace property and amenability for a class of banach algebras anthony to ming lau and yong zhangabstract motivated by a result of ky fan in 1965 we establish a charac terization of a left amenable f algebra which includes the group algebra andthe fourier algebra of a locally compact group and quantum group algebras or more generally the predual algebra of a hopf von neumann algebra interms of a nite dimensional invariant subspace property this is done by rstrevealing a xed point property for the semigroup of norm one positive lin ear functionals in the algebra our result answers an open question posted intokyo in 1993 by the rst author see 25 problem 5 we also show that theleft amenability of an ideal in an f algebra may determine the left amenabilityof the algebra

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

characterisations of fourier and fourier stieltjes algebras on locally compact groups abstract motivated by the beautiful work of m a rieffel 1965 and of m e walter 1974 we obtain characterisations of the fourier algebra a g of a locally compact group g in terms of the class of f algebras i e a banach algebra a such that its dual a is a w algebra whose identity is multiplicative on a for example we show that the fourier algebras are precisely those commutative semisimple f algebras that are tauberian contain a nonzero real element and possess a dual semigroup that acts transitively on their spectrums our characterisations fall into three flavours where the first one will be the basis of the other two the first flavour also implies a simple characterisation of when the predual of a hopf von neumann algebra is the fourier algebra of a locally compact group we also obtain similar characterisations of the fourier stieltjes algebras of g en route we prove some new results on the problem of when a subalgebra of a g is the whole algebra and on representations of discrete groups

power law persistence characterizes traveling waves in coupled circle maps with repulsive coupling we study persistence in coupled circle maps with repulsive inhibitory coupling and find that it offers an effective way to characterize the synchronous traveling wave and spatiotemporally chaotic states of the system in the traveling wave state persistence decays as a power law and in contrast to earlier observations in dynamical systems this power law scaling does not occur at the transition point alone but over the entire dynamical phase with the same exponent we give a cellular automata model displaying the qualitative features of the traveling wave regime and provide an argument based on the theory of motzkin numbers in combinatorics to explain the observed scaling

dynamic buckling of columns by biaxial moments and uniform end torque a new concept of uniform torque is proposed for the dynamic torsional buckling analysis a dynamic biaxial moments and torque buckling theory is presented for analysis in structural dynamics second order effects of the axial force biaxial moments and torque are considered the consistent natural boundary moments and forces are derived to ensure the symmetry of the dynamic stiffness matrix in fulfilling the requirement of the reciprocal theorem and conservation of energy the exact dynamic stiffness matrix is obtained using power series expansion the derivatives of the analytical dynamic stiffness matrix with respect to different loading and geometric parameters are derived explicitly for sensitivity and continuation analyses generally distributed axial force can be analyzed without difficulty it is pointed out that non uniform sections may not be handled by power series due to the convergent problem global pictures for all kinds of linear dynamic buckling are given for the first time the methodology is based on finite element formulation and therefore it can easily be extended to analyze structural frames

hopf bifurcation to repetitive activity in nerve various nerve axons and other excitable systems exhibit repetitive activity e g trains of propagated impulses in response to a spatially localized time independent stimulus if the stimulus is too weak or in some cases too strong one finds rather a spatially nonuniform steady response which attenuates with distance from the input site we consider these stimulus response properties for a qualitative model of nerve conduction the fitzhugh nagumo parabolic partial differential equations for each stimulus amplitude there is a unique steady state solution at critical stimulus values this steady solution loses stability and a branch of time periodic spatially nonuniform solutions appears via hopf bifurcation we associate this with the onset of repetitive activity we derive analytic bifurcation formulae and evaluate these for the case of a cubic nonlinearity to determine regions in parameter space where the steady solution is unstable we interpret physiologically the effect of stimulus form e

an approximate formula for the fundamental frequency of a uniform rotating beam clamped off the axis of rotation a semi empirical method involving asymptotic expansions is used to obtain an approximate formula for the fundamental frequency of a uniform rotating beam clamped off the axis of rotation results from the formula are shown to be of the order of 0 1 different length thus the designer is provided with a rapid very accurate estimate of the frequency without having to interpolate results from a chart or run a digital computer program

fourier stieltjes algebra of a topological group abstract this paper is an invitation to the study of the fourier stieltjes algebra b g the linear span of the continuous positive definite complex valued functions on a topological group g we study b g when g has a host algebra or a group c algebra the analogue of the group c algebra of a locally compact group our main challenge is that a topological group g cannot have a positive regular borel measure which is left translation invariant unless g is locally compact

coupling induced resonance in two mutually and asymmetrically coupled oscillators we consider two mutually coupled oscillators where we have independent control over the magnitude sign and delay of the coupling signal for appropriate tuning of the coupling constants there is a coupling induced resonance where the amplitude becomes large we investigate the role of nonlinear dissipation and amplitude dependent frequency correction on the coupling resonance with delayed coupling we track the deformation of the resonant bifurcation equation through imperfect bifurcations and the generation of isolas which generate intervals of multistability between oscillations of different amplitudes the resonance should be observable in coupled oscillator systems where the amplitude remains an important dynamical variable but not in limit cycle oscillators modeled by phase only descriptions

sungular hopf bifurcation to relaxation oscillations this paper is a continuation of our study of singular hopf bifurcations to relaxation oscillations siam journal on applied mathematics 46 1986 pp 721 739 in our previous analysis a system of two first order nonlinear equatins is investigated and it is shown how the bifurcation problem can be reduced to a weakly perturbed conservative system of two first order equations in this paper a method based on analyzing nearly conservative quantities was developed to find the bifurcation diagram of the periodic solutions emerging from singular hopf bifurcation points specifically the subcritical hopf bifurcation of the fitzhugh nagumo equations is analyzed the extension from the earlier bifurcation analysis is achieved by performing a perturbation analysis from the first integral of the leading order nonlinear oscillator at a critical value of a parameter the first integral exists up to an additional order in the perturbed equation this condition permits the resolution of features determined by h

isometries between jb triples let z and w be jb triples and let t be a linear isometry from z into w for any z z with z 1 we show that