the minimal period problem for nonconvex even second order hamiltonian systems abstract in this paper we study the minimal period problem for even autonomous second order hamiltonian systems defined on r nwithout any convexity assumption by using the variational methods we obtain estimates on the minimal period of the corresponding nonconstant periodic solution of the superquadratic and asymptotically linear hamiltonian systems

analytic derivatives for estimation of linear dynamic models abstract this paper develops two algorithms algorithm 1 computes the exact gaussian log likelihood function its exact gradient vector and an asymptotic approximation of its hessian matrix for discrete time linear dynamic models in state space form algorithm 2 derived from algorithm 1 computes the exact sample information matrix of this likelihood function the computed quantities are analytic not numerical approximations and should therefore be useful for reliably quickly and accurately i checking local identifiability of parameters by checking the rank of the information matrix ii using the gradient vector and hessian matrix to compute maximum likelihood estimates of parameters with newton methods and iii computing asymptotic covariances cramer rao bounds of the parameter estimates with the hessian or the information matrix the principal contribution of the paper is algorithm 2 which extends to multivariate models the univariate results of porat and friedlander 1 by relying on the kalman filter instead of the levinson durbin filter used by porat and friedlander algorithms 1 and 2 can automatically handle any pattern of missing or linearly aggregated data although algorithm 1 is well known it is treated in detail in order to make the paper self contained

analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

tensor sylvester matrices and the fisher information matrix of varmax processes the purpose of this paper is to develop compact expressions for the fisher information matrix fim of a gaussian stationary vector autoregressive and moving average process with exogenous or input variables a vector armax or varmax process we develop a representation of the fim based on multiple sylvester matrices an extension of this representation yields another one but in terms of tensor sylvester matrices in order to obtain the results presented in this paper the approach used in a klein g melard p spreij on the resultant property of the fisher information matrix of a vector arma process linear algebra appl 403 2005 291 313 is extended

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

on a theorem of weinstein abstract this paper contains an existence theorem for a special class of periodic solutions of hamiltonian systems and generalizes an earlier result of the same nature due to weinstein he studied a general class of mechanical systems and established the existence of special kinds of periodic solutions which he called brake orbits roughly speaking these solutions start at the boundary of a potential well with 0 velocity and return to the edge of the well again with 0 velocity a half period later this paper contains a generalization of his results using minimax methods form the calculus of variations as the existence tool

on the pressure transfer function for solitary water waves with vorticity in this paper we analyse the role which the pressure function on the sea bed plays in determining solitary waves with vorticity we prove that the pressure function on the flat bed determines a unique real analytic solitary wave solution to the governing equations given a real analytic vorticity distribution in particular the pressure function on the flat bed prescribes a unique surface profile for the resulting solitary water wave

relative morse index and multiple brake orbits of asymptotically linear hamiltonian systems in the presence of symmetries in this paper we define a relative morse index for two continuous symmetric matrices paths in r 2n satisfying condition b1 and study its relation with the maslov type indices under brake orbit boundary value of these two symmetric matrices paths as applications using this relation we obtain a multiple existence of periodic brake orbit solutions of asymptotically linear hamiltonian system in the presence of symmetries

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

on the existence of periodic solutions for a class of symetric hamiltonian systems abstract hamiltonian systems are used to model the motion of discrete mechanical systems this paper establishes the existence of periodic solutions for a class of such systems the method developed to prove existence should be useful for other such problems keywords minimax technique ordinary differential equations and variational problem

symmetry of steady periodic gravity water waves with vorticity we prove that steady periodic two dimensional rotational gravity water waves with a monotone surface profile between troughs and crests have to be symmetric about the crest irrespective of the vorticity distribution within the fluid

on the existence of extreme waves and the stokes conjecture with vorticity this is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity we show that for a certain class of vorticity functions a sequence of regular waves converges to an extreme wave with stagnation points at its crests we also show that for any vorticity function the profile of an extreme wave must have either a corner of 120 or a horizontal tangent at any stagnation point about which it is supposed symmetric moreover the profile necessarily has a corner of 120 if the vorticity is nonnegative near the free surface

recovering the water wave profile from pressure measurements a new method is proposed to recover the water wave surface elevation from pressure data obtained at the bottom of the fluid the new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the surface elevation which is obtained from the euler formulation of the water wave problem without approximation from this new equation a variety of different asymptotic formulas are derived the nonlocal equation and the asymptotic formulas are compared with both numerical data and physical experiments the solvability properties of the nonlocal equation are rigorously analyzed using the implicit function theorem

an explicit expression for the fisher information matrix of a multiple time series process the principal result in this paper is concerned with the derivative of a vector with respect to a block vector or matrix this is applied to the asymptotic fisher information matrix fim of a stationary vector autoregressive and moving average time series process varma representations which can be used for computing the components of the fim are then obtained in a related paper a klein a generalization of whittle s formula for the information matrix of vector mixed time series linear algebra appl 321 2000 197 208 the derivative is taken with respect to a vector this is obtained by vectorizing the appropriate matrix products whereas in this paper the corresponding matrix products are left unchanged

on the normal exponential map in singular conformal metrics abstract brake orbits and homoclinics of autonomous dynamical systems correspond via maupertuis principle to geodesics in riemannian manifolds endowed with a metric which is singular on the boundary jacobi metric motivated by the classical yet still intriguing in many aspects problem of establishing multiplicity results for brake orbits and homoclinics as done in giambo et al 2005 2010 2011 and by the development of a morse theory in giambo et al 2014 for geodesics in such kind of metric in this paper we study the related normal exponential map from a global perspective

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

rotation type solutions for spatially periodic hamiltonian systems along with solutions of 0 2 and in general for o l the hamiltonian h also called the energy is conserved this one dimensional situation can be studied in the phase space that is r x s since the sine function is periodic when the energy his prescribed and bigger than 1 then system 0 2 has two periodic solutions these periodic solutions however are not homotopic to a constant and they are usually called rotation type solutions it is the purpose of this paper to generalize this situation to equation 0 1 spatially periodic hamiltonian systems have been studied by several authors the nonautonomous case of 0 1 has been considered in l 7 for the existence of periodic solutions see also references therein the papers of liu s and the author 3 are specially related to this work there the existence of periodic solutions is established through a generalized saddle point theorem the hypotheses on h assumed in 3 will be considered here

homoclinic solutions of hamiltonian systems with symmetry abstract we prove the existence of infinitely many homoclinic solutions for a first order hamiltonian system symmetric with respect to an action of a compact lie group by means of variational methods we make no convexity assumption on the hamiltonian

matrix differential calculus applied to multiple stationary time series and an extended whittle formula for information matrices abstract the purpose of this paper is to set forth easily implementable expressions for the fisher information matrix fim of a gaussian stationary vector autoregressive and moving average process with exogenous or input variables a vector armax or varmax process the entries of the fim are represented as circular integral expressions and can be computed by applying cauchy s residue theorem an extension of the whittle formula for the fim of multiple time series processes is developed for varmax processes it will be shown that the extended whittle formula yields the fim when a bivariate structure consisting of the varmax process and the exogenous input process is considered consequently the equivalence between a frequency and time domain representation of the fim of varmax processes is established in order to obtain the results presented in this paper the differentiation techniques developed and used in a klein p spreij an explicit expression for the fisher information matrix of a multiple time series process linear algebra appl 417 2006 140 149 are applied

construction of the exact fisher information matrix of gaussian time series models by means of matrix differential rules the fisher information matrix is of fundamental importance for the analysis of parameter estimation of time series models in this paper the exact information matrix of a multivariate gaussian time series model expressed in state space form is derived a computationally efficient procedure is used by applying matrix differential rules for the derivatives of a matrix function j j with respect to its vector argument an algorithm is given it is sketched for the general state space structure without specifying a parametrization it is then detailed for the vector autoregressive moving average varma model with a given parametrization where explicit recurrent relations are developed

multiple brake orbits in bounded convex symmetric domains abstract in this paper we prove that there exist at least two geometrically distinct brake orbits in every bounded convex symmetric domain in r n for n 2

an index theory and existence of multiple brake orbits for star shaped hamiltonian systems soit h r 2n r une fonction continument differentiable et j o i ou i est la matrice identite n n on considere le systeme hamiltonien x jh x on etudie l existence de solutions periodiques sur une hypersurface compacte donnee h 1 1

symmetrically homoclinic orbits for symmetric hamiltonian systems in this paper we study the existence of symmetric homoclinic orbits for first order and second order hamiltonian systems with some symmetric hamiltonian functions

infinite dimensional linking let n be a closed separable subspace of a hilbert space e we can define a new norm v w satisfying v w v v n and such that the topology induced by this norm is equivalent to the weak topology of n on bounded subsets of n this can be done as follows let ek be an orthonormal basis for n define displaystyle u v w sum k 1 infty frac u e k v e k 2 k quad u v in n

brief paper accuracy of linear multiple input multiple output mimo models obtained by maximum likelihood estimation in this paper we study the accuracy of linear multiple input multiple output mimo models obtained by maximum likelihood estimation we present a frequency domain representation for the information matrix for general linear mimo models we show that the variance of estimated parametric models for linear mimo systems satisfies a fundamental integral trade off this trade off is expressed as a multivariable water bed effect an extension to spectral estimation is also discussed

global bifurcations of critical orbits of g invariant strongly indefinite functionals abstract let h be a separable hilbert space which is an orthogonal representation of a compact lie group g and let h r be a g invariant strongly indefinite functional of the class c 1 to study critical orbits of we have defined the degree for g invariant strongly indefinite functionals which is an element of the euler ring u g using this degree we have formulated the rabinowitz alternative for g invariant strongly indefinite functionals the abstract results are applied to the study of global bifurcations of weak solutions of non cooperative systems of elliptic differential equations

existence of multiple normal mode trajectories on convex energy surfaces of even classical hamiltonian systems hamiltonian systems of n degrees of freedom for which the hamiltonian is a function that is even both in its joint n coordinate variables as well as in its joint n momentum variables are discussed for such systems the number of distinct trajectories which correspond to particular periodic solutions normal modes with the same energy is investigated to that end a constrained dual action principle is introduced applying min max methods to this variational problem several results are obtained among which the existence of at least n distinct trajectories if specific conditions are satisfied

on the covering of a hill s region by solutions in systems with gyroscopic forces abstract consider a lagrangian system with the lagrangian containing terms linear in velocity by analogy with the systems in celestial mechanics we call a bounded connected component of the possible motion area of such a system a hill s region suppose that the energy level is fixed and the corresponding hill s region is compact we present sufficient conditions under which any point in the hill s region can be connected with its boundary by a solution with the given energy the result is illustrated by examples from mechanics

a semilinear schrodinger equation in the presence of a magnetic field we consider the semilinear stationary schrodinger equation in a magnetic field i a 2u v x u g x u u in n where v is the scalar or electric potential and a is the vector or magnetic potential we study the existence of nontrivial solutions both in the critical and in the subcritical case respectively g x u u 2 2 and g x u c 1 u p 2 where 2 p 2 the results are obtained by variational methods for g critical we use constrained minimization and for subcritical g we employ a minimax type argument in the latter case we also study the existence of infinitely many geometrically distinct solutions

multiple solutions for noncooperative p x laplacian equations in rn involving the critical exponent abstract in this paper we study the multiplicity of solutions for a class of noncooperative p x laplacian equations in r n involving the critical exponent by using the limit index theory due to li y q li a limit index theory and its application nonlinear anal 25 1995 1371 1389 and concentration compactness principle we obtain a sequence of radially symmetric solutions

periodic orbits of hamiltonian systems on symmetric positive type hypersurfaces this paper discusses the existence and multiplicity of periodic orbits of hamiltonian systems on symmetric positive type hypersurfaces we prove that each such energy hypersurface carries at least one symmetric periodic orbit under some suitable pinching conditions we also get an existence result of multiple symmetric periodic orbits

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

a generalization of whittle s formula for the information matrix of vector mixed time series abstract in a pioneering paper whittle developed a formula for expressing fisher s information matrix of multivariate time series models cf p whittle j royal statist soc b 15 1953 125 139 it is described as a function of the spectral density of the time series process the existing relationship is extended to the whole matrix instead of one element and is related with a time domain alternative expression the latter derives fisher s information matrix from the log gaussian likelihood function the equivalence of both approaches frequency and time domain which is summarized in a theorem shows that a considerable reduction in matrix integrals is taking place when moving from the former to the latter the hermitian property of the matrices under study contributes to construct the link between the two approaches and the theorem is further illustrated by an example

seifert conjecture in the even convex case in this paper we prove that there exist at least n geometrically distinct brake orbits on every c2 compact convex symmetric hypersurface in 2n satisfying the reversible condition n with n diag in in as a consequence we show that if the hamiltonian function is convex and even then seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integern 2014 wiley periodicals inc

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

iteration theory of l index and multiplicity of brake orbits abstract in this paper we first establish the bott type iteration formulas and some abstract precise iteration formulas of the maslov type index theory associated with a lagrangian subspace for symplectic paths as an application we prove that there exist at least n 2 1 geometrically distinct brake orbits on every c 2 compact convex symmetric hypersurface in r 2 n satisfying the reversible condition n furthermore if all brake orbits on this hypersurface are nondegenerate then there are at least n geometrically distinct brake orbits on it as a consequence we show that there exist at least n 2 1 geometrically distinct brake orbits in every bounded convex symmetric domain in r n furthermore if all brake orbits in this domain are nondegenerate then there are at least n geometrically distinct brake orbits in it in the symmetric case we give a positive answer to the seifert conjecture of 1948 under a generic condition

extrema of the dynamic pressure in an irrotational stokes wave with underlying currents and infinite depth abstract in this paper we investigate the dynamic pressure in an irrotational stokes wave in flows of finite depth with uniform underlying currents and infinite depth without underlying currents respectively using the maximum principles in combination with exploiting some of the physical structures of the problem itself we prove that irrespectively of uniform underlying current infinite depth and wave amplitude the maximum and minimum of the dynamic pressure are attained at the wave crest and at the wave trough respectively

on the resultant property of the fisher information matrix of a vector arma process a matrix is called a multiple resultant matrix associated to two matrix polynomials when it becomes singular if and only if the two matrix polynomials have at least one common eigenvalue in this paper a new multiple resultant matrix is introduced it concerns the fisher information matrix fim of a stationary vector autoregressive and moving average time series process varma the two matrix polynomials are the autoregressive and the moving average matrix polynomials of the varma process in order to show that the fim is a multiple resultant matrix two new representations of the fim are derived to construct such representations appropriate matrix differential rules are applied the newly obtained representations are expressed in terms of the multiple sylvester matrix and the tensor sylvester matrix the representation of the fim expressed by the tensor sylvester matrix is used to prove that the fim becomes singular if and only if the autoregressive and moving average matrix polynomials have at least one common eigenvalue it then follows that the fim and the tensor sylvester matrix have equivalent singularity conditions in a simple numerical example it is shown however that the fim fails to detect common eigenvalues due to some kind of numerical instability whereas the tensor sylvester matrix reveals it clearly proving the usefulness of the results derived in this paper

brief paper on the accuracy in errors in variables identification compared to prediction error identification errors in variables estimation problems for single input single output systems with gaussian signals are considered in this contribution it is shown that the fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated furthermore it is shown that whittle s formula for the fisher information matrix can be represented as a gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators finally the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases i when the model includes white measurement noise on the input and the variance of the noise is estimated and ii when the model includes only measurement noise on the output in both cases asymptotically efficient estimators are assumed an explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output

solutions for a class of quasilinear choquard equations with hardy littlewood sobolev critical nonlinearity abstract in this article we consider the quasilinear choquard equation with critical nonlinearity in r n e 2 u v x u e 2 u u 2 r n u 2 2 x y d y u 2 2 2 u h x u u where 0 n n 3 2 2 n n 2 is the critical exponent in the sense of hardy littlewood sobolev inequality e is a real parameter by using a change of variables the quasilinear equations are reduced to a semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem under suitable assumptions on v and h we investigate the existence and multiplicity of solutions for the above problem by using the mountain pass theorem and index theory in order to overcome the lack of compactness we apply the concentration compactness principle