evolution of a multimodal map induced by an equivariant vector field it has been shown that the topological characterization of an equivariant system should preferably be achieved by working in a fundamental domain generated by the symmetry properties appearing in the phase space in this paper we discuss the case when the equivariance of the studied system is taken into account to study the evolution of the population of periodic orbits when a control parameter is varied the burke shaw system is considered here as an example it is shown that the equivariance of this system may be used to reduce the multimodal first return map in a poincare section to a unimodal map a relationship between four symbol sequences and two symbol sequences is given the non trivial evolution of the orbit spectrum of a multimodal map is then predicted from the much simpler unimodal map to which the multimodal map reduces

on the symbolic dynamics of the henon map the authors study a method for finding all periodic orbits of the dissipative henon map for the canonical values a 1 4 b 0 3 this method is found to give indeed the good symbolic dynamics proposed earlier by two of them but it does not work as proposed for larger values of b this is seen in two ways although the method is thus not universally valid it can be used to study problems related to periodic orbits they find that for the usual values a 1 4 b 0 3 expressions for average quantities are not easily obtained precisely from periodic orbits in agreement with recent claims

precise asymptotic of eigenvalues of resonant quasilinear systems in this work we study the sequence of variational eigenvalues of a system of resonant type involving p and q laplacians on rn with a coupling term depending on two parameters and satisfying p q 1 we show that the order of growth of the kth eigenvalue depends on k o k n

dynamics of field driven interfaces in the two dimensional ising model the time dependent properties of an inclined interface separating up and down spin regions in a two dimensional nearest neighbour ising model evolving under glauber dynamics in a non zero field are studied in the limit of large exchange coupling the model reduces to the single step model for ballistic growth and thence to the asymmetric exclusion process which describes a driven diffusive system of hard core particles on a one dimensional lattice the drift velocity of the interface is found as a function of field temperature and inclination and interface correlation functions are related to sliding tag correlation functions in the particle system the existence of a critical value of the sliding tag velocity implies that there is an inclination dependent easy direction along which temporal interface fluctuations grow subdiffusively this direction is found as is the asymptotic behaviour of the correlation function in all other directions

estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems we consider solutions to the nonlinear eigenvalue problem a x u ui xf x j o ing2 u o on dol u 7 0o where is a quasilinear strongly coupled second order elliptic system of partial differential equations and q c ru is a smooth bounded domain we obtain lower bounds for x in the case where f x u has linear growth and relations between x s2 and ess sup i i when f yx u has subor superlinear growth the estimates are based on integration by parts and application of certain sobolev inequalities we briefly discuss extensions to higher order systems

lower bounds for generalized eigenvalues of the quasilinear systems abstract in this paper we establish several new lyapunov type inequalities for two classes of one dimensional quasilinear elliptic systems of resonant type which generalize or improve all related existing ones then we use the lyapunov type inequalities obtained in this paper to derive a better lower bound for the generalized eigenvalues of the one dimensional quasilinear elliptic system with the dirichlet boundary conditions

dynamical transitions of a driven ising interface we study the structure of an interface in a three dimensional ising system created by an external nonuniform field h r t h changes sign over a two dimensional plane of arbitrary orientation when the field is pulled with velocity v e i e h r t h r v e t the interface undergoes several dynamical transitions for low velocities it is pinned by the field profile and moves along with it the distribution of local slopes undergoing a series of commensurate incommensurate transitions for large v e the interface depins and grows with kardar parisi zhang exponents

the fredholm alternative at the first eigenvalue for the one dimensionalp laplacian abstract in this work we study the range of the operatoru u p 2 u 1 u p 2 u u 0 u t 0 p 1 we prove that all functionsh c1 0 t satisfying t0 h t sinp pt t dt 0 lie in the range but that ifp 2 andh 0 the solution set is bounded here sin pt t is a first eigenfunction associated to 1 we also show that in this case the associated energy functionalu 1 p t0 u p 1 p t0 u p t0 huis unbounded from below if 1 2 onw1 p0 0 t 1corresponds precisely to the best constant in thelp poincare inequality moreover we show that unlike the linear casep 2 forp 2 the range contains a nonempty open set inl 0 t

on the generalized spectrum for second order elliptic systems description qualitative et quantitative detaillee du spectre generalise reel pour les systemes elliptiques du second ordre application de la theorie des perturbations lineaires des methodes de prolongement et de la caracterisation variationnelle des valeurs propres de courant hilbert

exact field driven interface dynamics in the two dimensional stochastic ising model with helicoidal boundary conditions abstract we investigate the interface dynamics of the two dimensional stochastic ising model in an external field under helicoidal boundary conditions at sufficiently low temperatures and fields the dynamics of the interface is described by an exactly solvable high spin asymmetric quantum hamiltonian that is the infinitesimal generator of the zero range process generally the critical dynamics of the interface fluctuations is in the kardar parisi zhang universality class of critical behavior we remark that a whole family of rsos interface models similar to the ising interface model investigated here can be described by exactly solvable restricted high spin quantum x x z type hamiltonians

calculation of displacement correlation tensor indicating vortical cooperative motion in two dimensional colloidal liquids as an indicator of cooperative motion in a system of brownian particles that models two dimensional colloidal liquids a displacement correlation tensor is calculated analytically and compared with numerical results the key idea for the analytical calculation is to relate the displacement correlation tensor which is a kind of four point space time correlation to the lagrangian two time correlation of the deformation gradient tensor tensorial treatment of the statistical quantities including the displacement correlation itself allows capturing the vortical structure of the cooperative motion the calculated displacement correlation also implies a negative long time tail in the velocity autocorrelation which is a manifestation of the cage effect both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable suggesting that the cages are nested to form a self similar structure in the space time

eigenvalues of the p laplacian in fractal strings with indefinite weights in this paper we study the spectral counting function of the weighted p laplacian in fractal strings where the weight is allowed to change sign we obtain error estimates related to the interior minkowski dimension of the boundary we also find the asymptotic behavior of eigenvalues

profile driven interfaces in 1 1 dimensions periodic steady states dynamical melting and detachment abstract we study the steady state structure and dynamics of a 2 d ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity v e in the strong coupling limit the problem maps onto an asymmetric exclusion process involving motion of particles in 1 d with position dependent right and left jump probabilities for small v e the interface is stuck to the field profile as v e increases the profile detaches from the interface at the transition point and beyond the interfacial structure and dynamics are characterized by the kpz exponents for small v e on the other hand the interface is macroscopically smooth with a vanishing roughness exponent the interfacial structure is periodic with a periodicity which depends on the orientation of the interface for a fixed orientation this periodic structure melts as v e is increased we determine the dynamical phase diagram of this system in the v e orientation plane

the interpretation and measurement of the f α spectrum of a multifractal measure the authors analyse the growth probability distribution for differential limited aggregates dla in terms of its f curve and f and computed independently as generalized entropies using data from 10 clusters of 10000 to 100000 particles the growth probability is obtained by solving the laplace equations numerically with a hierarchical method which improves accuracy and speed two additional methods are used to compare results for dla clusters and for a few objects with simple geometry and known f spectrum these comparisons reinforce their results for the part of the dla spectrum corresponding to q0 they also bring to light some unexpected features for q 0 1 which suggest a non universality of the scaling exponents in this region in two dimensions

on the topology of the henon map topological invariants of the henon map are investigated by means of the pruning front first a long sequence of primary homoclinic tangencies is computed confirming the monotonicity of the front an algorithm to extract forbidden sequences is then introduced and discussed forbidden sequences of increasing lengths are used to construct a hierarchy of regular grammars represented by directed graphs which approximate the exact grammar arbitrarily well the topological entropy is estimated as the largest eigenvalue of their adjacency matrix it exhibits an exponential convergence towards the asymptotic value with an exponent in agreement with a previous conjecture based on the growth rate of the number of forbidden words

analytical calculation of four point correlations for a simple model of cages involving numerous particles dynamics of a one dimensional system of brownian particles with short range repulsive interaction diameter is studied with a liquid theoretical approach the mean square displacement the two particle displacement correlation and the overlap density based generalized susceptibility are calculated analytically by way of the lagrangian correlation of the interparticulate space instead of the eulerian correlation of density that is commonly used in the standard mode coupling theory in regard to the mean square displacement the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system a finite time correction is given by incorporating the effect of entropic nonlinearity with a lagrangian version of mode coupling theory the notorious difficulty in derivation of the mode coupling theory concerning violation of the fluctuation dissipation theorem is found to disappear by virtue of the lagrangian description the lagrangian description also facilitates analytical calculation of four point correlations in the space time such as the two particle displacement correlation the two particle displacement correlation which is asymptotically self similar in the space time illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand as the time elapses the correlation length grows unlimitedly and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density the distribution function behind these dynamical four point correlations and its extension to three dimensional cases respecting the tensorial character of the two particle displacement correlation are also discussed

the influence of elasticity on analysis modern developments on examine plusieurs domaines de l analyse auxquels l elasticite a apporte une contribution importante questions de connectivite de la theorie globale des bifurcations particularites de l analyse non lineaire calcul des variations convergence faible inegalites variationnelles autres contributions

dynamics for a two dimensional antisymmetric map a two dimensional representation of symbolic dynamics for a two dimensional map with antisymmetric property is constructed the behaviour of symmetry breaking periodic orbits symmetry breaking bifurcations symmetry breaking attractors and the boundaries of basins between co existing attractors are then discussed using this representation of symbolic dynamics

estimates for eigenvalues of quasilinear elliptic systems part ii abstract in this paper we find explicit lower bounds for dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p laplace equation also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value

simulation of domain wall dynamics in the 2d anisotropic ising model the authors first show that the movement of a domain wall in a highly anisotropic ising model of spins in two dimensions can be mapped to a random walk movement of labelled walkers in one dimension this movement is correlated in the sense that the transition probability of a given walker labelled i depends upon the current positions of its labelled neighbours i 1 and i 1 a monte carlo simulation of the walk for various numbers of walkers up to a maximum of 50 and for quite long times up to a maximum of 25 104 monte carlo steps yields useful and interesting information about the dynamics they verify that i the centre of mass of the walkers executes an unbiased random walk for all times starting from the lowest times and ii the moment of inertia of the walkers asymptotically reaches a constant value which scales with the number of walkers they also discuss the relation of this work to the dynamics in the 2d ising model identifying phi with the dynamical exponent z the random walk equivalence also provides a geometrical interpretation of the known results for the solid on solid model

a method for locating symmetric homoclinic orbits using symbolic dynamics in this paper we present a method which can identify and locate symmetric homoclinic orbits in a homoclinic tangle formed by the intersecting stable and unstable manifolds of a symmetric 2d map the method consists of a systematic search in parameter space and determination of the order in which these orbits arise using symbolic dynamics each orbit corresponds to a unique sequence and it is computed by iterating the map along the unstable manifold to match a specific symmetry at the middle of the orbit an application of the method to the determination of multibreather solutions of 1d lattices is discussed

on coupled multiparameter nonlinear elliptic systems on considere le systeme de problemes non lineaires aux valeurs limites de dirichlet lu x f u x v x lv x g u x v x x domaine borne de r n l est un operateur aux derivees partielles lineaire fortement et uniformement elliptique et sont des parametres reels f g r 2 r des applications continues telles que f 0 0 0 g 0 0 on presente une analyse detaillee de l ensemble des solutions du point de vue de la theorie de la bifurcation a plusieurs parametres

lyapunov type inequalities for partial differential equations in this work we present a lyapunov inequality for linear and quasilinear elliptic differential operators in n dimensional domains we also consider singular and degenerate elliptic problems with ap coefficients involving the p laplace operator with zero dirichlet boundary condition as an application of the inequalities obtained we derive lower bounds for the first eigenvalue of the p laplacian and compare them with the usual ones in the literature

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

two tag correlation functions in one dimensional lattice gases correlations between two labelled particles are studied in a one dimensional lattice gas with nearest neighbour hopping fluctuations in the distance between the first particle at time t and the other at time 0 are studied analytically and by monte carlo with unbiased and biased hopping in the latter case the tag tag correlation shows a nonmonotonic dependence on t a stochastic harmonic theory based on an exact mapping to an interface model suggests a scaling form for the correlation as a function of t and the difference between the labels monte carlo data are consistent with scaling in the unbiased case the scaling function given by the harmonic theory seems to be exact