nonexistence of formal first integrals for nonlinear systems under the case of resonance in this paper by using the normal form theory we give some criteria of the nonexistence of formal first integrals for nonlinear systems under resonance as application we also give a criterion for nonintegrability of a family of higher order perturbation systems of certain integrable hamiltonian systems

normal forms and bifurcations of planar vector fields normal forms and bifurcations of planar vector fields by s n chow c li and d wang cambridge university press cambridge and new york 1994 viii 472 pp 69 95 isbn 0 521 37226 7

integrals of motion for three dimensional non hamiltonian dynamical systems the problem of finding integrals of motion of three dimensional dynamical systems is analysed the authors introduce a new type of direct method in the search of parameter values for which an integral of motion exists this method consists in proposing an ansatz for the integral that explicitly shows the dependence with respect to one of the phase space coordinates of the system they apply this procedure to the reduced three wave interaction problem and to the rabinovich system for both models new integrals of motion are found

multiplicity of positive periodic solutions to superlinear repulsive singular equations abstract in this paper we study positive periodic solutions to the repulsive singular perturbations of the hill equations it is proved that such a perturbation problem has at least two positive periodic solutions when the anti maximum principle holds for the hill operator and the perturbation is superlinear at infinity the proof relies on a nonlinear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cones

a decoupled approach to illumination robust optical flow estimation despite continuous improvements in optical flow in the last three decades the ability for optical flow algorithms to handle illumination variation is still an unsolved challenge to improve the ability to interpret apparent object motion in video containing illumination variation an illumination robust optical flow method is designed this method decouples brightness into reflectance and illumination components using a stochastic technique reflectance is given higher weight to ensure robustness against illumination which is suppressed illumination experiments using the middlebury and university of oulu databases demonstrate the decoupled method s improvement when compared with state of the art in addition a novel technique is implemented to visualize optical flow output which is especially useful to compare different optical flow methods in the absence of the ground truth

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

painleve property and geometry abstract the painleve property for discrete hamiltonian systems implies the existence of a symplectic manifold which augments the original phase space and on which the flows exist and are analytic for all times the augmented manifold is constructed by expanding the hamilton jacobi equation a complete classification of the types of poles allowed in complex time is given for hamiltonians which separate into the direct product of hyperelliptic curves for such systems bounds on the degrees of the polynomial separating variable change and the other integrals in involution can be found from the pole series and the hamilton jacobi equation it is shown how branching can arise naturally in a painleve system

on the number of isolating integrals in perturbed hamiltonian systems with n or 3 degrees of freedom we consider a perturbed hamiltonian system with n or 3 degrees of freedom of the form h h0 epsilon h1 and show that the properties of the average value of the perturbing function h1 along the periodic orbits of the unperturbed integrable part h0 supply criteria for non integrability which restrict the allowed total number of independent integrals of motion

positive periodic solutions of functional differential equations with impulses and a parameter by applying the well known leggett williams multiple fixed point theorem this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter

local first integrals for systems of differential equations the main purpose of this paper is to provide some sufficient conditions for a system of differential equations to have local first integrals in a certain neighbourhood of a singularity our results generalize those given in kwek et al 2003 z angew math phys 54 26 and li et al 2003 z angew math phys 54 235

invariant algebraic surfaces of the lorenz system in this paper we provide a complete classification of the darboux invariants of the irreducible darboux polynomials of the rational first integrals and of the algebraic integrability for the classical lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

on the nonintegrability of yang mils potentials the nonintegrability of three hamiltonian systems obtained by simplifications of the yang mills classical field theory is proved by application of two theorems of yoshida 1987 1988 it is also shown that for the two four degree of freedom systems there exists a set of three independent integrals of motion in involution

nonexistence of formal first integrals for general nonlinear systems under resonance abstract in this paper we consider the nonintegrability for nonlinear systems under the simple resonant case i e the jacobian matrix of vector field at some fixed point has some single multiply zero eigenvalues and some nonzero eigenvalues which are n independent by using the poincare dulac normal form theory we give a necessary condition for the system under consideration to have formal first integral

positive periodic solutions of delayed differential equations abstract in this paper we are concerned with the existence multiplicity and nonexistence of positive periodic solutions of the following equation u t a t u u t b t f u t t t r where a c r r r is a periodic function with respect to the first variable b c r 0 c r r all are periodic functions f c 0 0 and f s 0 for s 0 0 is a parameter the proof of our main results is based upon fixed point index theory

importance weighted marginal bayesian posterior density estimation abstract markov chain sampling schemes generate dependent observations i 0 i n from a full joint posterior distribution data frequently only certain marginals of this full posterior density are of interest thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations i 0 i n from data we propose a new importance weighted marginal density estimation iwmde method an iwmde is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w the asymptotic properties for the iwmde and the guidelines for choosing a weighting conditional density w are also considered a bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the iwmde s for the marginal posterior densities

highly accurate optic flow computation with theoretically justified warping in this paper we suggest a variational model for optic flow computation based on non linearised and higher order constancy assumptions besides the common grey value constancy assumption also gradient constancy as well as the constancy of the hessian and the laplacian are proposed since the model strictly refrains from a linearisation of these assumptions it is also capable to deal with large displacements for the minimisation of the rather complex energy functional we present an efficient numerical scheme employing two nested fixed point iterations following a coarse to fine strategy it turns out that there is a theoretical foundation of so called warping techniques hitherto justified only on an experimental basis since our algorithm consists of the integration of various concepts ranging from different constancy assumptions to numerical implementation issues a detailed account of the effect of each of these concepts is included in the experimental section the superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

on the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems in this paper we first give a necessary condition for general nonlinear systems to have rational first integrals then by using the so called kowalevsky exponents we present a criterion for nonexistence of rational first integrals for semiquasihomogeneous systems

positive periodic solutions of second order nonlinear differential systems with two parameters by employing the deimling fixed point index theory we consider a class of second order nonlinear differential systems with two parameters l m r 2 0 0 we show that there exist three nonempty subsets of r 2 0 0 c d 1 and d 2 such that r 2 0 0 c d 1 d 2 and the system has at least two positive periodic solutions for l m d 1 one positive periodic solution for l m c and no positive periodic solutions for l m d 2 meanwhile we find two straight lines l 1 and l 2 such that c lies between l 1 and l 2

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

liouvillian first integrals of differential equations liouvillian functions are functions that are built up from rational functions using exponentiation integration and algebraic functions we show that if a system of differential equations has a generic solution that satisfies a liouvillian relation that is there is a liouvillian function of several variables vanishing on the curve defined by this solution then the system has a liouvillian first integral that is a nonconstant liouvillian function that is constant on solution curves in some nonempty open set we can refine this result in special cases to show that the first integral must be of a very special form

on the polynomial integrability of the hoyer systems abstract the hoyer polynomial differential systems depend on nine parameters we provide the necessary conditions in order that these systems have two functionally independent polynomial first integrals we show that these conditions are not sufficient additionally we illustrate how the polynomial first integrals of these systems can be computed using the kowalevsky exponents

integrating the nonintegrable analytic structure of the lorenz system revisited abstract a study of the complex time analytic structure of the lorenz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one time dependent integral of motion exists furthermore the analysis yields the exact form of the part of the integral with the highest homogeneous weight and a method to construct the rest of the integral recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument the analytic techniques used in these studies a systematic resummation of a logarithmic psi series appears to be quite general and can provide explicit representations of a solution even in the chaotic regimes in the neighborhood of a given movable singularity furthermore we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems

the singularity analysis for nearly integrable systems homoclinic intersections and local multivaluedness abstract in this study a new perturbative scheme for nonintegrable ordinary differential equations is proposed these perturbative expansions are based on the singularity analysis of the unperturbed system and is performed in the neighborhood of its singularities under suitable conditions on the homoclinic structure of the unperturbed system the melnikov vector can be computed based on the knowledge of the laurent expansions of the solutions the existence of transverse homoclinic intersections is therefore explicitly related to the existence of critical points for the solutions in the complex plane of the independent variable

on the integrability of two dimensional flows this paper deals with the notion of integrability of flows or vector fields on two dimensional manifolds we consider the following two key points about first integrals 1 they must be defined on the whole domain of definition of the flow or vector field or defined on the complement of some special orbits of the system 2 how are they computed we prove that every local flow on a two dimensional manifold m always has a continuous first integral on each component of m where is the set of all separatrices of we consider the inverse integrating factor and we show that it is better to work with it instead of working directly with a first integral or an integrating factor for studying the integrability of a given two dimensional flow or vector field finally we prove the existence and uniqueness of an analytic inverse integrating factor in a neighborhood of a strong focus of a non resonant hyperbolic node and of a siegel hyperbolic saddle

formal first integrals for periodic systems in the present paper we give an elementary proof for the result of li et al 2003 6 about nonexistence of formal first integrals for periodic systems in a neighborhood of a constant solution moreover we present a criterion about partial existence of formal first integrals for the periodic system by using the floquet s theory

a criterion for the non existence of an additional integral in hamiltonian systems with a homogeneous potential abstract a non integrability criterion on the basis of ziglin s theorem is given for two degrees of freedom hamiltonians with a homogeneous potential of integer degree as simple examples the anisotropic kepler problem and the one dimensional newtonian three body problem are proved to be non integrable a self contained proof of ziglin s theorem n dimensional homogeneous potential version is also given

integrals of quadratic ordinary differential equations in r3 the lotka volterra system abstract a method already introduced by the last two authors for finding the integrable cases of three dimensional autonomous ordinary differential equations based on the frobenius integrability theorem is described in detail using this method and computer algebra the so called three dimensional lotka volterra system is studied many cases of integrability are thus found the study of this system is completed by the application of painleve analysis and the jacobi last multiplier method the methods used are of general interest and can be applied to many other systems

on the complete and partial integrability of non hamiltonian systems abstract the methods of singularity analysis are applied to several third order non hamiltonian systems of physical significance including the lotka volterra equations the three wave interaction and the rikitake dynamo model complete integrability is defined and new completely integrable systems are discovered by means of the painleve property in all these cases we obtain integrals which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation ode solved by painleve transcendents relaxing the painleve property we find many partially integrable cases whose movable singularities are poles at leading order with in t t 0 terms entering at higher orders in an n th order generalized rossler model a precise relation is established between the partial fulfillment of the painleve conditions and the existence of n 2 integrals of the motion

integrability partial integrability and nonintegrability for systems of ordinary differential equations the integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods three types of results are obtained first a general relationship between the degrees of first integrals and the so called kowalevskaya exponents is derived second it is shown that all solutions of algebraically integrable systems can be expanded in puiseux series third a new method to study partially integrable systems is studied these different aspects allow us to study algorithmically the integrability partial integrability and nonintegrability of differential systems

computing optical flow with physical models of brightness variation although most optical flow techniques presume brightness constancy it is well known that this constraint is often violated producing poor estimates of image motion this paper describes a generalized formulation of optical flow estimation based on models of brightness variations that are caused by time dependent physical processes these include changing surface orientation with respect to a directional illuminant motion of the illuminant and physical models of heat transport in infrared images with these models we simultaneously estimate the 2d image motion and the relevant physical parameters of the brightness change model the estimation problem is formulated using total least squares with confidence bounds on the parameters experiments in four domains with both synthetic and natural inputs show how this formulation produces superior estimates of the 2d image motion

on the polynomial integrability of kirchoff s equations abstract we prove that kirchoff s equations either are completely integrable or have at most four functionally independent polynomial first integrals

on the nonexistence of rational first integrals for systems of linear differential equations abstract we present a description of all systems of linear differential equations which do not admit any rational first integral

symmetries and first integrals for dissipative systems the connection between symmetries time independent and time dependent first integrals for autonomous systems of first order ordinary differential equations is discussed several new results which have been obtained by applying a reduce package are reported

periodic solutions for scalar functional differential equations suf ficient criteria are established f or the existence ofpositive periodic solutions ofscalar f tional differential equations which improve and generalize some related results in the literature the approach is based on the krasnoselskii s fixed point theorem numerical simulations are presented to support the analytical analysis 2005 elsevier ltd all rights reserved msc 34k13 92d25

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

periodic solutions of second order non autonomous singular dynamical systems abstract in this paper we establish two different existence results of positive periodic solutions for second order non autonomous singular dynamical systems the first one is based on a nonlinear alternative principle of leray schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity the second one is based on schauder s fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions recent results in the literature are generalized and significantly improved