nonlinear panel flutter by finite element method les equations non lineaires sont calculees a partir de considerations energetiques et la force d etirement non lineaire est formulee en termes de deplacement transversal seul

limits of hypercyclic and supercyclic operators abstract an operator t on a complex separable infinite dimensional hilbert space h is hypercyclic if there is a vector y in h such that the orbit y ty t2y is dense in h it is shown that if t is hypercyclic then t does not have any eigenvalue and that the union of the spectrum of t and the unit circle is a connected set this result is used to obtain a spectral characterization of the norm closure of the class hc h of all hypercyclic operators acting on h as well as a formula for the distance from a given operator to hc h analogous results are obtained for the closely related class sc h of all supercyclic operators this paper includes some information about the structure of the set of all hypercyclic supercyclic vectors of a given hypercyclic supercyclic resp operator t

proper orthogonal decomposition method for analysis of nonlinear panel flutter with thermal effects in supersonic flow abstract the proper orthogonal decomposition pod method for analysis of nonlinear panel flutter subjected to supersonic flow is presented optimal pod modes are extracted from a chaotic galerkin mode responses the aeroelastic equations of motion are constructed using von karman plate theory first order piston theory and quasi steady thermal stress theory a simply supported plate with thermal loads from a uniformly distributed temperature is considered many types of panel behaviors including stable flat dynamically stable buckled limit cycle oscillation nonharmonic periodic motion quasi periodic motion and chaotic motion are observed our primary focus is on chaos and the route to chaos it is found that a sudden transition from the buckled state to chaos occurs time history phase portrait poincare map bifurcation diagram and lyapunov exponent are employed to study chaos the pod chaotic results obtained are compared with the traditional galerkin solutions it is shown that the pod method can obtain accurate chaotic solutions using fewer modes and less computational effort than the galerkin mode approach additionally the pod method converges faster in the analysis of chaotic transients effects of length to width ratios and thermal loads are presented it is found that a smaller width for fixed length will produce more stable flutter response while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions the numerical simulations show that the robustness of the pod modes depends on the dynamic pressure but not on temperature

mean ergodic composition operators on banach spaces of holomorphic functions abstract given a symbol i e a holomorphic endomorphism of the unit disc we consider the composition operator c f f defined on the banach spaces of holomorphic functions a d and h d we obtain different conditions on the symbol which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces these conditions are related to the asymptotic behavior of the iterates of the symbol finally we deal with some particular case in the setting of weighted banach spaces of holomorphic functions

on universal subsets of banach spaces we prove that to most of the known hypercyclic operators a on separable banach spaces there exist compact compact convex compact connected subsets k of e such that each compact compact convex compact connected subset of e can be approximated with respect to hausdorff s distance by a n k for suitable n in mathbb n

on the stability of periodic orbits of two dimensional mappings we present a closed form stability criterion for the periodic orbits of two dimensional conservative as well as dissipative mappings which are analogous to the poincare maps of dynamical systems our stability criterion has a particularly simple form involving a finite symmetric nearly tridiagonal determinant its derivation is based on an extension of the stability analysis of hill s differential equation to difference equations we apply our criterion and derive a sufficient stability condition for a large class of periodic orbits of the widely studied standard mapping describing a periodically kicked free rotator as another example we also obtain explicitly and in closed form the intervals of bounded and unbounded solutions of a discrete schrodinger equation for the kronig and penney crystal model

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

hypercyclic bilinear operators on banach spaces abstract we study the dynamics induced by an m linear operator we answer a question of bes and conejero showing an example of an m linear hypercyclic operator acting on a banach space moreover we prove the existence of m linear hypercyclic operators on arbitrary infinite dimensional separable banach spaces we also prove an existence result about symmetric bihypercyclic bilinear operators answering a question by grosse erdmann and kim

semi fredholm theory hypercyclic and supercyclic subspaces a vector x in a banach space cal b is called hypercyclic for a bounded linear operator t cal b rightarrow cal b if the orbit t n x n geq 1 is dense in cal b we prove that if t is hereditarily hypercyclic and its essential spectrum meets the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is also true even if t is not hereditarily hypercyclic in this way we improve and extend to banach spaces a recent result for hilbert spaces we also investigate the corresponding problem for supercyclic operators in this case we obtain a description of the norm closure of the class of all supercyclic operators that have an infinite dimensional closed subspace of hypercyclic vectors moreover for certain kinds of supercyclic operators we can characterize when they have an infinite dimensional closed subspace of supercyclic vectors 1991 mathematics subject classification 47b38 47b99

nonlinear panel flutter using high order triangular finite elements a 54 degree of freedom high order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems the finite element formulation is based on kirchhoffs theory of thin plates the quasisteady aerodynamic theory is used numerical solution procedures are presented the limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped respectively the effects of in plane compressive force mass ratio and in plane edge stress free condition are considered stress distributions for the limit cycle oscillation of a two dimensional panel are plotted for the case of panels under static pressure differential the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels respectively the effect of biaxial in plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region dynamically stable buckled region and the limit cycle oscillation region are found alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

bifurcations and chaos in the ϕ4 theory on a lattice the authors have studied numerically and analytically the discrete phi 4 model defined by bak and pokrovsky see phys rev lett vol 47 no 13 p 958 61 1981 the model may describe peierls systems structural instabilities metal insulator transitions etc in solid state physics the phi 4 theory can be formulated as an area preserving two dimensional mapping this mapping exhibits infinite series of period doubling bifurcation leading to chaos the bifurcations are characterised by universal numbers delta 8 72109 and alpha 4 0180 which appear to be identical to those found by bountis 1981 for the henon mapping but different from the feigenbaum numbers for dissipative systems in addition novel features arise because of marginally stable fixed points and the splitting of one 2 cycle orbit into two 2 cycle orbits

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

stacking sequence design of flat composite panel for flutter and thermal buckling in this paper we formulate the stacking sequence design of laminated composite flat panels for maximum supersonic flutter speed and maximum thermal buckling capacity the design is constrained to have stable limit cycle oscillation in the vicinity of the flutter boundary for the purpose of comparison we consider both linear and nonlinear panel flutter analyses because of manufacturing constraints the stacking sequence of the laminate is selected from a discrete set of orientation angles the plate is modeled using von karman plate equations and assumed to be subjected to uniform temperature differential the aerodynamic load on the plate is computed using third order piston theory the plate equations of motion are derived using hamilton s principle and discretized using the rayleigh ritz method the nonlinear panel flutter analysis is performed using an approximate perturbation approach the pareto fronts describing the trade off between thermal buckling and flutter are generated for different panel aspect ratios it is observed that optimal designs obtained for both linear and nonlinear flutter analyses are similar with only the predicted flutter speeds different this suggests that for the purpose of preliminary stacking sequence design linear flutter analysis is sufficient

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

period multiplying bifurcations and multifurcations in conservative mappings the authors have investigated numerically and analytically the period doubling bifurcations and multifurcations of the periodic orbits of the conservative sine gordon mappings they have derived a general equation for the appearance of multifurcations in conservative mappings in agreement with many recent studies they also find evidence that such mappings possess universality properties they also discuss the role of multifurcations in conservative mappings exhibiting chaotic behaviour

cyclicity of bicyclic operators and completeness of translates we study cyclicity of operators on a separable banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions a simple consequence of our main result is that a bicyclic unitary operator on a banach space with separable dual is cyclic our results also imply that if s a n n in mathbb z longmapsto a n 1 n in mathbb z is the shift operator acting on the weighted space of sequences ell omega 2 mathbb z if the weight satisfies some regularity conditions and n 1 for nonnegative n then s is cyclic if rm lim n rightarrow infty rm log omega n sqrt n 0 on the other hand one can see that s is not cyclic if the series sum n geq 1 rm log omega n n 2 diverges we show that the question of herrero whether either s or s is cyclic on ell omega 2 mathbb z admits a positive answer when the series sum n in mathbb z rm log s n n 2 1 is convergent we also prove completeness results for translates in certain banach spaces of functions on mathbb r

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

existence of common and upper frequently hypercyclic subspaces abstract we provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces which include the following consequences there exist frequently hypercyclic operators with upper frequently hypercyclic subspaces and no frequently hypercyclic subspace on the space of entire functions each differentiation operator induced by a non constant polynomial supports an upper frequently hypercyclic subspace and the family of its non zero scalar multiples has a common hypercyclic subspace a question of costakis and sambarino on the existence of a common hypercyclic subspace for a certain uncountable family of weighted shift operators is also answered

hypercyclic tuples of operators and somewhere dense orbits in this paper we prove that there are hypercyclic n 1 tuples of diagonal matrices on cn and that there are no hypercyclic n tuples of diagonalizable matrices on cn we use the last result to show that there are no hypercyclic subnormal tuples in infinite dimensions we then show that on real hilbert spaces there are tuples with somewhere dense orbits that are not dense but we also give sufficient conditions on a tuple to insure that a somewhere dense orbit on a real or complex space must be dense

hypercyclic operators on non normable frechet spaces abstract every infinite dimensional separable non normable frechet space admits a continuous hypercyclic operator a large class of separable countable inductive limits of banach spaces with the same property is given but an example of a separable complete inductive limit of banach spaces which admits no hypercyclic operator is provided it is also proved that no compact operator on a locally convex space is hypercyclic

chaos in numerical analysis of ordinary differential equations abstract the discretisation of the ordinary nonlinear differential equation d y d t y 1 y by the entral difference scheme is studied for fixed mesh size in the usual numerical computation this method produces some ghost solution for the long range calculation regarding this discretisation as a dynamical system in r2 these pathological behaviors are shown to be a kind of chaos in the dynamical system for any mesh size moreover some combination of the central difference scheme and the euler s scheme is studied for the above equation it gives some motivation for henon s model the usual discretisation of a second order differential equation are studied also it gives some chaotic behaviors numerically which is similar to the behavior of the orbits of the system of differential equations proposed by henon heiles

a dynamical characterization of sub arakelian subsets abstract we are going to characterize those sets which can be covered by an arakelian set in terms of dynamical properties of entire functions via similarities moreover if we consider the set of universal entire functions via similarities that are bounded on such a sub arakelian set then it is shown that its algebraic size is as large as possible as a consequence we prove that the set of universal entire functions bounded on every straight line is algebraically large

a nonlinear age and maturity structured model of population dynamics i basic theory a nonlinear model of age and maturity structured population dynamics is analyzed the population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth the existence and asymptotic behavior of solutions are studied

linear structure of hypercyclic vectors abstract a vector x in a banach space b is called hypercyclic for a bounded linear operator t b b if the orbit t n x n 1 is dense in b our main result states that if t is a compact perturbation of an operator of norm 1 and satisfies an appropiate extra hypothesis then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t in particular the result applies to compact perturbations of the identity we also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts this last result in combination with a recent one that states that every banach space admits an operator with a hypercyclic vector proves that in all banach space there is an operator t with an infinite dimensional closed subspace consisting except for zero of hypercyclic vectors the main result also applies to the differentiation operator and the translation operator t f z f z 1 on certain hilbert spaces consisting of entire functions

some remarks on abstract universal series abstract we introduce a new class of universal series in the abstract setting this class lies between two already known classes of universal series by two examples we differentiate these classes these examples are the first examples in the case where all classes are non void we also prove that the class of universal series where the approximating indexes have upper density 1 is dense and g and that the class of lower frequently universal series is of the first category

proper orthogonal decomposition reduced order model for nonlinear aeroelastic oscillations in this study the proper orthogonal decomposition method in conjunction with a galerkin projection scheme is employed to solve the title problem of a fluttering plate in both two and three dimensions undergoing supersonic flow using von karman s large deflection plate theory and quasi steady supersonic aerodynamic theory proper orthogonal decomposition based reduced order models are constructed by using the responses as snapshots from the conventional galerkin method which also plays a role as a reference method in this paper results for the buckled limit cycle oscillation and chaotic responses of the simply supported plate are presented and compared with the galerkin solutions numerical examples demonstrate that the proper orthogonal decomposition reduced order model permits a much lower dimensional model as compared to that obtainable via the galerkin approach for example for a plate length to width ratio equal to 4 only two proper orthogonal decomposition modes are required to describe the pa

optimal growth of entire functions frequently hypercyclic for the differentiation operator we solve a problem posed by bonilla and grosse erdmann 2007 7 by constructing an entire function f which is frequently hypercyclic with respect to the differentiation operator and satisfies mf r cerr 1 4 where c 0 may be chosen arbitrarily small this growth rate is sharp we also obtain optimal results for minimal growth in terms of average lp norms among other tools the proof uses the rudin shapiro polynomials and heat kernel estimates

hypercyclicity and chaotic left multiplication mappings on operator spaces let x be a separable infinite dimensional banach space and b x b e the algebra of all bounded linear operators on x for any t b x define a left multiplication mapping lt b x b x b ylt v tv v b x we give a hypercyclicity criterion on b x and in addition if x is a banach space with a symmetric basis we give a similar criterion on its dual space x we also investigate the connections between hypercyclic and chaotic behavior of lt on b x and that of t on x and prove that t is chaotic in the sense of devaney if and only if the left multiplication operator lt is chaotic

finite element analysis of large amplitude panel flutter of thin laminates the principle of virtual work is used to develop the equations of motion the large deflections are represented by von karman strain displacement relations and the aerodynamic load is represented by the use of the quasisteady first order piston theory the equations of motion are solved by implementing the lineared updated mode with a nonlinear time function lum ntf approximation critical flutter values and limit cycle amplitudes for graphite epoxy and boron epoxy laminates are investigated

period doubling bifurcations and universality in conservative systems we have studied numerically a sequence of period doubling bifurcations of periodic orbits of henon s conservative two dimensional mapping in agreement with other recent studies we also find evidence that such sequences possess universality properties similar to the ones observed for dissipative systems the corresponding universal constants however have significantly different values in each case we suggest that a possible explanation for this discrepancy may be the fact that conservative systems owing to their measure preserving property do not become asymptotically one dimensional as dissipative systems do

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

universal entire functions for affine endomorphisms of c n abstract in this paper the affine endomorphisms of c n which support compositionally universal entire functions are completely characterized

a generalization of universal taylor series in simply connected domains abstract let be a simply connected proper subdomain of the complex plane and z 0 be a point in it is known that there are holomorphic functions f on for which the partial sums s n f z 0 of the taylor series about z 0 have universal approximation properties outside in this paper we investigate what can be said for the sequence n s n f z 0 when n is a sequence of complex numbers we also study a related analogue of a classical theorem of seleznev concerning the case where the radius of convergence of the universal power series is zero

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

spectral theory and hypercyclic subspaces a vector x in a hilbert space h is called hypercyclic for a bounded operator t h h if the orbit tnx n 1 is dense in h our main result states that if t satisfies the hypercyclicity criterion and the essential spectrum intersects the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is true even if t is a hypercyclic operator which does not satisfy the hypercyclicity criterion as a consequence other characterizations are obtained for an operator t to have an infinite dimensional closed subspace of hypercyclic vectors these results apply to most of the hypercyclic operators that have appeared in the literature in particular they apply to bilateral and backward weighted shifts perturbations of the identity by backward weighted shifts multiplication operators and composition operators the main result also applies to the differentiation operator and the translation operator t f z f z 1 defined on certain hilbert spaces consisting of entire functions we also obtain a spectral characterization of the norm closure of the class of hypercyclic operators which have an infinite dimensional closed subspace of hypercyclic vectors

universal and chaotic multipliers on spaces of operators we use tensor product techniques to study universality hypercyclicity and chaos of multipliers defined on operator ideals and of multiplication operators on the space of all continuous and linear operators thus continuing the work of kit chan we also obtain the first examples of outer multipliers on a banach algebra which are chaotic in the sense of devaney and prove sufficient conditions for the existence of closed subspaces of universal vectors for operators between frechet spaces

on a universality property of certain integral operators in this paper we establish a universality property of fourier and hankel convolution operators and dunkl transforms

non sequential weak supercyclicity and hypercyclicity abstract a bounded linear operator t acting on a banach space b is called weakly hypercyclic if there exists x b such that the orbit t n x n 0 1 is weakly dense in b and t is called weakly supercyclic if there is x b for which the projective orbit t n x c n 0 1 is weakly dense in b if weak density is replaced by weak sequential density then t is said to be weakly sequentially hypercyclic or supercyclic respectively it is shown that on a separable hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic this is achieved by constructing a borel probability measure on the unit circle for which the fourier coefficients vanish at infinity and the multiplication operator m f z z f z acting on l 2 is weakly supercyclic it is not weakly sequentially supercyclic since the projective orbit under m of each element in l 2 is weakly sequentially closed this answers a question posed by bayart and matheron it is proved that the bilateral shift on l p z 1 p is weakly supercyclic if and only if 2 p and that any weakly supercyclic weighted bilateral shift on l p z for 1 p 2 is norm supercyclic it is also shown that any weakly hypercyclic weighted bilateral shift on l p z for 1 p 2 is norm hypercyclic which answers a question of chan and sanders