design and application of reduced order adaptive observer with exponential rate of convergence for single input single output linear systems abstract this paper is concerned with the design of an adaptive observer to estimate state variables and identify parameters of an unknown linear single input single output system with desired rate of exponential convergence the observer structure is based on the kreisselmeier types representation of parametrized form but the adaptive law is obtained by a new scheme the adaptive law is determined by equations forcing the errors into decreasing exponentially and it is designed to guarantee the asymptotic stability of the identification and estimation processes globally a method of reducing the order of the adaptive law is also proposed the reduction of the order is executed by using a priori information regarding relations between the unknown parameters an experimental application using a heated tank with water jacket is included to show the practical effectiveness of the reduced order adaptive scheme

simultaneous parameter tracking and state estimation in a linear system abstract the task of simultaneous tracking of time varying parameters and estimation of the state is treated for a linear system described by a time varying input output armax or delta model with known c noise parameters first a bayesian approach based conceptual solution is presented then it is shown that utilizing the properties of the observer canonical state model algebraic recursion operating on the joint parameter and state mean and covariance matrix can be obtained with no approximation involved several illustrative examples are included

stable bundles and integrable systems on considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de riemann on montre que ce sont des systemes dynamiques hamiltoniens algebriquement completement integrables

duality between the trigonometric bcn sutherland system and a completed rational ruijsenaars schneider van diejen system we present a new case of duality between integrable many body systems where two systems live on the action angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other one our investigation utilizes an idea that was exploited previously to provide group theoretic interpretation for several dualities discovered originally by ruijsenaars in the group theoretic framework one applies hamiltonian reduction to two abelian poisson algebras of invariants on a higher dimensional phase space and identifies their reductions as action and position variables of two integrable systems living on two different models of the single reduced phase space taking the cotangent bundle of u 2n as the upstairs space we demonstrate how this mechanism leads to a new dual pair involving the bcn trigonometric sutherland system thereby we generalize earlier results pertaining to the an trigonometric sutherland system as well as a recent work by pusztai on the hyperbolic bcn sutherland system

scattering theory for the federbush massless thirring and continuum ising models the existence of the lsz limits of the positive energy quantum fields of the federbush thirring and ising models is proved the corresponding s matrices are obtained explicitly confirming previous formal results and are shown to result from a large class of dynamics the scattering theory for the federbush and thirring models on the classical and negative energy quantum levels is studied as well the wave and scattering operators are shown to exist and are obtained explicitly and they are proved to be shared by a large class of dynamics containing in particular the polynomial conserved charges

the finite toda lattices connection is established between one dimensional toda lattices constructed on the basis of the systems of simple roots of classical and affine lie algebras and other integrable systems of interacting particles that connection allows us to find new lattices differing from the known ones by the interaction of particles near the ends some of the new lattices admit non abelian generalizations

fillings of unit cotangent bundles we study the topology of exact and stein fillings of the canonical contact structure on the unit cotangent bundle of a closed surface sigma g where g is at least 2 in particular we prove a uniqueness theorem asserting that any stein filling must be s cobordant rel boundary to the disk cotangent bundle of sigma g for exact fillings we show that the rational homology agrees with that of the disk cotangent bundle and that the integral homology takes on finitely many possible values including that of dt sigma g for example if g 1 is square free then any exact filling has the same integral homology and intersection form as dt sigma g

dualities in integrable systems and n 2 susy theories we discuss dualities in the integrable dynamics behind the exact solution to the n 2 susy yang mills theory it is shown that t duality in the string theory is related to the separation of variables procedure in the dynamical system we argue that there are analogues of s duality as well as three dimensional mirror symmetry in the many body systems of hitchin type governing the low energy effective actions

a discrete adaptive observer for a system of unknown order a discrete adaptive observer for a single input single output linear system is described the order of the system is unknown except that it is not greater than some preassigned integer the observer finds the system order estimates the parameters in output canonical form and gives the estimated state vector at each sample step

on the quantization of a self dual integrable system in this note we apply canonical quantization to the self dual particle system describing the motion of poles to a higher rank solution of the kp hierarchy explicitly determining both the quantum hamiltonian and the wavefunction it is verified that the quantum hamiltonian is trivially bispectral that is that the wavefunction can be taken to be symmetric as predicted by a widely held hypothesis of mathematical physics

noncommutative extensions of elliptic integrable euler arnold tops and painleve vi equation in this paper we suggest generalizations of elliptic integrable tops to matrix valued variables our consideration is based on the r matrix description which provides lax pairs in terms of quantum and classical r matrices first we prove that for relativistic and non relativistic tops such lax pairs with spectral parameters follow from the associative yang baxter equation and its degenerations then we proceed to matrix extensions of the models and find out that some additional constraints are required for their construction we describe a matrix version of the reduced elliptic top and verify that the latter constraints are fulfilled in this case the construction of matrix extensions is naturally generalized to the monodromy preserving equation in this way we get matrix extensions of the painleve vi equation and its multidimensional analogues written in the form of non autonomous elliptic tops finally it is mentioned that the matrix valued variables can be replaced by elements of noncommutative associative algebra at the end of the paper we also describe special elliptic gaudin models which can be considered as matrix extensions of the reduced elliptic top

kernel functions and backlund transformations for relativistic calogero moser and toda systems we obtain kernel functions associated with the quantum relativistic toda systems both for the periodic version and for the nonperiodic version with its dual this involves taking limits of previously known results concerning kernel functions for the elliptic and hyperbolic relativistic calogero moser systems we show that the special kernel functions at issue admit a limit that yields generating functions of backlund transformations for the classical relativistic calogero moser and toda systems we also obtain the nonrelativistic counterparts of our results which tie in with previous results in the literature

holomorphic bundles and many body systems we show that spin generalization of elliptic calogero moser system elliptic extension of gaudin model and their cousins are the degenerations of hitchin systems applications to the constructions of integrals of motion angle action variables and quantum systems are discussed the constructions of classical systems are motivated by conformal field theory and their quantum counterparts can be thought of as being the degenerations of the critical level knizhnik zamolodchikov bernard equations

symplectic manifolds with contact type boundaries an example of a 4 dimensional symplectic manifold with disconnected boundary of contact type is constructed a collection of other results about symplectic manifolds with contact type boundaries are derived using the theory ofj holomorphic spheres in particular the following theorem of eliashberg floer mcduff is proved if a neighbourhood of the boundary of v is symplectomorphic to a neighbourhood ofs2n 1 in standard euclidean space and if vanishes on all 2 spheres inv thenv is diffeomorphic to the ballb2n

bihamiltonian structures and quadratic algebras in hydrodynamics and on non commutative torus we demonstrate the common bihamiltonian nature of several integrable systems the first one is an elliptic rotator that is an integrable euler arnold top on the complex group gl n open image in new window for any n whose inertia ellipsiod is related to a choice of an elliptic curve its bihamiltonian structure is provided by the compatible linear and quadratic poisson brackets both of which are governed by the belavin drinfeld classical elliptic r matrix we also generalize this bihamiltonian construction of integrable euler arnold tops to several infinite dimensional groups appearing as certain large n limits of gl n open image in new window these are the group of a non commutative torus nct and the group of symplectomorphisms sdiff t2 of the two dimensional torus the elliptic rotator on symplectomorphisms gives an elliptic version of an ideal 2d hydrodynamics which turns out to be an integrable system in particular we define the quadratic poisson algebra on the space of hamiltonians on t2 depending on two irrational numbers in conclusion we quantize the infinite dimensional quadratic poisson algebra in a fashion similar to the corresponding finite dimensional case

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

the lax pairs for elliptic cn and bcn ruijsenaars schneider models and their spectral curves we study the elliptic c n and bcn ruijsenaars schneider models which are elliptic generalization of systems given in previous paper by the present authors chen j math phys 41 8132 2000 the lax pairs for these models are constructed by hamiltonian reduction technology we show that the spectral curves can be parametrized by the involutive integrals of motion for these models taking nonrelativistic limit and scaling limit we verify that they lead to the systems corresponding to calogero moser and toda types c 2001 american institute of physics

on the arnold conjecture for weakly monotone symplectic manifolds we show the arnold conjecture concerning symplectic fixed points in the case that the symplectic manifold is weakly monotone and all the fixed points are non degenerate in particular the conjecture is true in dimension 2 4 6 if all the fixed points are non degenerate

integrable discretizations of the spin ruijsenaars schneider models integrable discretizations are introduced for the rational and hyperbolic spin ruijsenaars schneider models these discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous time counterparts explicit solutions are obtained for arbitrary flows of the hierarchies including the discrete time ones

floer novikov homology and applications to lagrangian submanifolds we use a non hamiltonian version of lagrangian floer homology to prove that an exact lagrangian submanifold in the cotangent bundle of the 3 torus t 3 must be diffeomorphic to t 3 this improves a previous result of fukaya seidel and smith

reduction of the elliptic sl n mathbb c top we propose a relation between the elliptic top and toda systems and obtain a new class of integrable systems in a specific limit of the elliptic top the relation is based on the inozemtsev limit and a symplectic map from the elliptic calogero moser system to the elliptic top in the case when n 2 we use an explicit form of a symplectic map from the phase space of the elliptic calogero moser system to the phase space of the elliptic top and show that the limiting tops are equivalent to the toda chains in the case when n 2 we generalize the above procedure using only the limiting behavior of lax matrices in a specific limit we also obtain a more general class of systems and prove the integrability in the liouville sense of a certain subclass of these systems this class is described by a classical r matrix obtained from an elliptic r matrix

integrability of difference calogero moser systems a general class of n particle difference calogero moser systems with elliptic potentials is introduced besides the step size and two periods the hamiltonian depends on nine coupling constants we prove the quantum integrability of the model for n 2 and present partial results for n 3 in degenerate cases rational hyperbolic or trigonometric limit the integrability follows for arbitrary particle number from previous work connected with the multivariable q polynomials of koornwinder and macdonald liouville integrability of the corresponding classical systems follows as a corollary limit transitions lead to various well known models such as the nonrelativistic calogero moser systems associated with classical root systems and the relativistic calogero moser system

gromov s compactness of pseudo holomorphic curves and symplectic geometry on utilise certaines idees de schoerr et uhlenbeck sur les equations aux derivees partielles pour demontrer la compacite de gromov des courbes pseudoholomorphes

hilbert schmidt operators vs integrable systems of elliptic calogero moser type ii the an 1 case first steps this is the second part of a series of papers concerning hilbert schmidt integral operators acting on the hilbert spaces associated with elliptic calogero moser type hamiltonians we present an explicit diagonalization of special hilbert schmidt operators arising in the free an 1 case and a spectral structure analysis of the commut ing family of hilbert schmidt operators associated with the general an 1 case

relativistic toda systems we present and study poincare invariant generalizations of the galilei invariant toda systems the classical nonperiodic systems are solved by means of an explicit action angle transformation

characteristic classes and hitchin systems general construction we consider topologically non trivial higgs g bundles over riemann surfaces g with marked points and the corresponding hitchin systems we show that if g is not simply connected then there exists a finite number of different sectors of the higgs bundles endowed with the hitchin hamiltonians they correspond to different characteristic classes of the underlying bundles defined as elements of h 2 sigma g mathcal z g mathcal z g is a center of g we define the conformal version cg of g an analog of gl n for sl n and relate the characteristic classes with degrees of cg bundles we describe explicitly bundles in the genus one g 1 case if 1 has one marked point and the bundles are trivial then the hitchin systems coincide with calogero moser cm systems for the nontrivial bundles we call the corresponding systems the modified calogero moser mcm systems their phase space has the same dimension as the phase space of the cm systems with spin variables but less number of particles and greater number of spin variables starting with these bundles we construct lax operators quadratic hamiltonians and define the phase spaces and the poisson structure using dynamical r matrices the latter are completion of the classification list of etingof varchenko corresponding to the trivial bundles to describe the systems we use a special basis in the lie algebras that generalizes the basis of t hooft matrices for sl n we find that the mcm systems contain the standard cm subsystems related to some unbroken subalgebras the configuration space of the cm particles is the moduli space of the stable holomorphic bundles with non trivial characteristic classes

action angle maps and scattering theory for some finite dimensional integrable systems i the pure soliton case we construct an action angle transformation for the calogero moser systems with repulsive potentials and for relativistic generalizations thereof this map is shown to be closely related to the wave transformations for a large classl of hamiltonians and is shown to have remarkable duality properties all dynamics inl lead to the same scattering transformation which is obtained explicitly and exhibits a soliton structure an auxiliary result concerns the spectral asymptotics of matrices of the formm exp td ast it pertains to diagonal matricesd whose diagonal elements have pairwise different real parts and to matricesm for which certain principal minors are non zero

weak and strong fillability of higher dimensional contact manifolds for contact manifolds in dimension three the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent we extend these facts to higher dimensions in particular we define a natural generalization of weak fillings and prove that it is indeed weaker at least in dimension five while also being obstructed by all known manifestations of overtwistedness we also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense these depend on a higher dimensional analogue of giroux torsion which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions abstract starting from the hyperoctahedral multivariate hypergeometric function of heckman and opdam associated with the b c n root system we arrive via partial confluent limits in the sense of oshima and shimeno at solutions of the eigenvalue equations for the quantum toda chain with one sided boundary perturbations of poschl teller type and for the hyperbolic quantum calogero sutherland system in a morse potential with the aid of corresponding degenerations of the bispectral dual difference equations for the heckman opdam hyperoctahedral hypergeometric function it is deduced that the eigensolutions in question are holomorphic in the spectral variable

on the duality between the hyperbolic sutherland and the rational ruijsenaars schneider models we consider two families of commuting hamiltonians on the cotangent bundle of the group and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic sutherland and of the rational ruijsenaars schneider lax matrices respectively the duality symplectomorphism between these two integrable models that was constructed by ruijsenaars using direct methods can then be interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group

symmetry algebras for superintegrable systems it is shown that the symmetry algebra of quantum maximally superintegrable systems can always be chosen to be u n n being the number of degrees of freedom

factorized weight functions vs factorized scattering starting from an extensive class of factorized weight functions w p on the n dimensional torus we construct an orthonormal base of symmetric n variable polynomials for l 2 s w p dp via lexicographic ordering of the monomial symmetric functions free boson states and the gram schmidt procedure we show that the dominant asymptotics of these polynomials is factorized as a corollary we obtain a large class of quantum integrable soliton systems on the symmetric subspace of l 2 n the class of weight functions contains in particular the weight function yielding macdonald polynomials for that special case the quantum soliton system can be viewed as the dual relativistic calogero sutherland system

discrete adaptive observer with exponential weighting properties an adaptive observer based on the exponentially weighted least squares method is studied and a method of selecting the state variable filters is proposed by this method all the past measurement data are weighted exponentially both with weighting coefficient and the state variable filters the proposed scheme guarantees fast convergence and is very stable

quiver text w _ boldsymbol epsilon _ mathbf 1 boldsymbol epsilon _ mathbf 2 algebras of 4d boldsymbol mathcal n mathbf mathbf 2 gauge theories we construct an e deformation of w algebras corresponding to the additive version of quiver w q t algebras which feature prominently in the 5d version of the bps cft correspondence and refined topological strings on toric calabi yau s this new type of algebras fill in the missing intermediate level between q deformed and ordinary w algebras we show that e deformed w algebras are spectral duals of conventional w algebras in particular the e deformed conformal blocks manifestly reproduce instanton partition functions of 4d n 2 quiver gauge theories in the full background and give dual integral representations of ordinary w conformal blocks

contact structures on product five manifolds and fibre sums along circles two constructions of contact manifolds are presented i products of s1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and ii fibre connected sums along isotropic circles baykur has found a decomposition as required for i for all closed oriented 4 manifolds as a corollary we can show that all closed oriented 5 manifolds that are cartesian products of lower dimensional manifolds carry a contact structure for symplectic 4 manifolds we exhibit an alternative construction of such a decomposition this gives us control over the homotopy type of the corresponding contact structure in particular we prove that mathbb cp 2 times s 1 admits a contact structure in every homotopy class of almost contact structures the existence of contact structures is also established for a large class of 5 manifolds with fundamental group mathbb z 2

painleve vi rigid tops and reflection equation we show that the painleve vi equation has an equivalent form of the non autonomous zhukovsky volterra gyrostat this system is a generalization of the euler top in mathbb c 3 and includes the additional constant gyrostat momentum the quantization of its autonomous version is achieved by the reflection equation the corresponding quadratic algebra generalizes the sklyanin algebra as by product we define integrable xyz spin chain on a finite lattice with new boundary conditions

on geometric phases for soliton equations this paper develops a new complex hamiltonian structure forn soliton solutions for a class of integrable equations such as the nonlinear schrodinger sine gordon and korteweg de vries hierarchies of equations that yields amongst other things geometric phases in the sense of hannay and berry for example one of the possible soliton geometric phases is manifested by the well known phase shift that occurs for interacting solitons the main new tools are complex angle representations that linearize the corresponding hamiltonian flows on associated noncompact jacobi varieties this new structure is obtained by taking appropriate limits of the differential equations describing the class of quasi periodic solutions a method of asymptotic reduction of the angle representations is introduced for investigating soliton geometric phases that are related to the presence of monodromy at singularities in the space of parameters in particular the phase shift of interacting solitons can be expressed as an integral over a cycle on an associated riemann surface in this setting soliton geometric asymptotics are constructed for studying geometric phases in the quantum case the general approach is worked out in detail for the three specific hierarchies of equations mentioned some links with functions the braid group and geometric quantization are pointed out as well

poisson lie interpretation of trigonometric ruijsenaars duality a geometric interpretation of the duality between two real forms of the complex trigonometric ruijsenaars schneider system is presented the phase spaces of the systems in duality are viewed as two different models of the same reduced phase space arising from a suitable symplectic reduction of the standard heisenberg double of u n the collections of commuting hamiltonians of the systems in duality are shown to descend from two families of free hamiltonians on the double which are dual to each other in a poisson lie sense our results give rise to a major simplification of ruijsenaars proof of the crucial symplectomorphism property of the duality map

hitchin systems symplectic hecke correspondence and two dimensional version the aim of this paper is two fold first we define symplectic maps between hitchin systems related to holomorphic bundles of different degrees we call these maps the symplectic hecke correspondence shc of the corresponding higgs bundles they are constructed by means of the modification of the underlying holomorphic bundles shc allows to construct backlund transformations in the hitchin systems defined over riemann curves with marked points we apply the general scheme to the elliptic calogero moser cm system and construct shc to an integrable sl n euler arnold top the elliptic sl n rotator next we propose a generalization of the hitchin approach to 2d integrable theories related to the higgs bundles of infinite rank the main example is an integrable two dimensional version of the two body elliptic cm system the previous construction allows us to define shc between the two dimensional elliptic cm system and the landau lifshitz equation

the geometry of symplectic energy non squeezing theorem which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form r2 x b2 where b2 is a 2 disc this led to hofer s discovery of symplectic capacities which give a way of measuring the size of subsets in symplectic manifolds recently hofer found a way to measure the size or energy of symplectic diffeomorphisms by looking at the total variation of their generating hamiltonians this gives rise to a bi invariant pseudo norm on the group ham m of compactly supported hamiltonian symplectomorphisms of the manifold m the deep fact is that this pseudo norm is a norm in other words the only symplectomorphism on m with zero energy is the identity map up to now this had been proved only for sufficiently nice symplectic manifolds and by rather complicated analytic arguments in this paper we consider a more geometric version of this energy which was first considered by eliashberg and hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary we prove by a simple geometric argument that both versions of energy give rise to genuine norms on all symplectic manifolds roughly speaking we show that if there were a symplectomorphism of m which had too little energy one could embed a large ball into a thin cylinder m x

vector bundles and lax equations on algebraic curves the hamiltonian theory of zero curvature equations with spectral parameter on an arbitrary compact riemann surface is constructed it is shown that the equations can be seen as commuting flows of an infinite dimensional field generalization of the hitchin system the field analog of the elliptic calogero moser system is proposed an explicit parameterization of hitchin system based on the tyurin parameters for stable holomorphic vector bundles on algebraic curves is obtained

rational top and its classical r matrix we construct a rational integrable system the rational top on a co adjoint orbit of sl n lie group it is described by the lax operator with spectral parameter and classical non dynamical skew symmetric r matrix in the case of the orbit of minimal dimension the model is gauge equivalent to the rational calogero moser cm system to obtain the results we represent the lax operator of the cm model in two different factorized forms without spectral parameter related to the spinless case and another one with the spectral parameter the latter gives rise to the rational top while the first one is related to generalized cremmer gervais r matrices the gauge transformation relating the rational top and cm model provides the classical rational version of the irf vertex correspondence from the geometrical point of view it describes the modification of bundles over degenerated elliptic curve in view of the symplectic hecke correspondence the rational top is related to the rational spin cm model possible applications and generalizations of the suggested construction are discussed in particular the obtained r matrix defines a class of kzb equations

generalized lame functions ii hyperbolic and trigonometric specializations in part i j math phys 40 1595 1999 we studied eigenfunctions of the quantum dynamics that defines the two particle relativistic calogero moser system with elliptic interaction in the present paper we consider the same system with hyperbolic and trigonometric interactions in these special regimes the eigenfunctions are shown to admit an elementary representation that is far more explicit than the zero representation of part i in particular the new representation can be exploited to prove that the hyperbolic eigenfunctions can be chosen to be symmetric under interchanging position and momentum variables self duality in the trigonometric case duality properties are derived too and several orthogonality and completeness results are obtained

difference equation for the heckman opdam hypergeometric function and its confluent whittaker limit abstract we present an explicit difference equation for the heckman opdam hypergeometric function associated with root systems via a confluent hypergeometric limit an analogous difference equation is obtained for the class one whittaker function diagonalizing the open quantum toda chain

the dn ruijsenaars schneider model the lax pair of the ruijsenaars schneider model with interaction potential of trigonometric type based on dn lie algebra is presented we give a general form for the lax pair and prove partial results for small n liouville integrability of the corresponding system follows a series of involutive hamiltonians generated by the characteristic polynomial of the lax matrix the rational case appears as a natural degeneration and the non relativistic limit exactly leads to the well known calogero moser system associated with dn lie algebra

trigonometric sutherland systems and their ruijsenaars duals from symplectic reduction beside its usual interpretation as a system of n indistinguishable particles moving on the circle the trigonometric sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line and these three physically distinct systems are in duality with corresponding variants of the rational ruijsenaars schneider system we explain that the three duality relations first obtained by ruijsenaars in 1995 arise naturally from the kazhdan kostant sternberg symplectic reductions of the cotangent bundles of the group u n and its covering groups u 1 su n and r su n respectively this geometric interpretation enhances our understanding of the duality relations and simplifies ruijsenaars original direct arguments that led to their discovery

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

self duality and scattering map for the hyperbolic van diejen systems with two coupling parameters with an appendix by s ruijsenaars in this paper we construct global action angle variables for a certain two parameter family of hyperbolic van diejen systems following ruijsenaars ideas on the translation invariant models the proposed action angle variables come from a thorough analysis of the commutation relation obeyed by the lax matrix whereas the proof of their canonicity is based on the study of the scattering theory as a consequence we show that the van diejen system of our interest is self dual with a factorized scattering map also in an appendix by s ruijsenaars a novel proof of the spectral asymptotics of certain exponential type matrix flows is presented this result is of crucial importance in our scattering theoretical analysis

sharp estimates of the kobayashi metric and gromov hyperbolicity abstract let d 0 be a smooth relatively compact domain in a four dimensional almost complex manifold m j where is a j plurisubharmonic function on a neighborhood of d and strictly j plurisubharmonic on a neighborhood of d we give sharp estimates of the kobayashi metric our approach is based on an asymptotic quantitative description of both the domain d and the almost complex structure j near a boundary point following z m balogh and m bonk z m balogh m bonk gromov hyperbolicity and the kobayashi metric on strictly pseudoconvex domains comment math helv 75 2000 504 533 these sharp estimates provide the gromov hyperbolicity of the domain d

the structure of rational and ruled symplectic 4 manifolds this paper investigates the structure of compact symplectic 4 manifolds v w which contain a symplectically embedded copy c of s2 with nonnegative self intersection number such a pair v c w is called minimal if in addition the open manifold v c contains no exceptional curves i e symplectically embedded 2 spheres with self intersection 1 we show that every such pair v c w covers a minimal pair v c c which may be obtained from v by blowing down a finite number of disjoint exceptional curves in v c further the family of manifold pairs v c w under consideration is closed under blowing up and down we next give a complete list of the possible minimal pairs we show that v is symplectomorphic either to p2 with its standard form or to an s2 bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class moreover this symplectomorphism may be chosen so that it takes c either to 2 a complex line or quadric in cp2 or in the case when v is a bundle to a fiber or section of the bundle department of mathematics state university of new york at stony brook stony brook new york 11794 3651 e mail address dusa math sunysb edu this content downloaded from 207 46 13 145 on wed 27 apr 2016 05 10 07 utc all use subject to http about jstor org terms

structures in bcn ruijsenaars schneider models we construct the classical r matrix structure for the lax formulation of bcn ruijsenaars schneider systems proposed in commun math phys 115 127 1988 the r matrix structure takes a quadratic form similar to the an ruijsenaars schneider poisson bracket behavior although the dynamical dependence is more complicated commuting hamiltonians stemming from the bcn ruijsenaars schneider lax matrix are shown to be linear combinations of particular koornwinder van diejen external fields ruijsenaars schneider models for specific values of the exponential one body couplings uniqueness of such commuting hamiltonians is established once the first of them and the general analytic structure are given

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

rationally convex domains and singular lagrangian surfaces in mathbb c 2 we give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in mathbb c 2 we recall some classical obstructions and prove some deeper ones related to symplectic and contact topology we explain the close connection to lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces our proof also gives a complete characterization of lagrangian surfaces with open whitney umbrellas answering a question first posed by givental in 1986

double coset construction of moduli space of holomorphic bundles and hitchin systems we present a description of the moduli space of holomorphic vector bundles over riemann curves as a double coset space which is differ from the standard loop group construction our approach is based on equivalent definitions of holomorphic bundles based on the transition maps or on the first order differential operators using this approach we present two independent derivations of the hitchin integrable systems we define a superfree upstairs system from which hitchin systems are obtained by three step hamiltonian reductions special attention is given to the schottky parameterization of curves

symplectic diffeomorphisms and the flux homomorphism let x be a connected smooth manifold without boundary we will write difff ox for the group of all compactly supported diffeomorphisms of x which preserve the symplectic form o2 topologized as usual as the direct limit of the subgroups diff x of all diffeomorphisms with support in the fixed compact set k let diff oox be its identity component the flux is locally a homomorphism from a neighbourhood of the identity in diffo ox to h x r see calabi 6 it gives rise to a global homomorphism s o from the universal cover of difffo0x to hi x f and hence to a homomorphism

the monge ampere equation on almost complex manifolds we study the dirichlet problem for the monge ampere equation on almost complex manifolds we obtain the existence of the unique smooth solution in strictly pseudoconvex domains

r matrix structure of hitchin system in tyurin parameterization we present a classical r matrix for the hitchin system without marked points on an arbitrary non degenerate algebraic curve of genus g 2 using tyurin parameterization of holomorphic vector bundles

the non dynamical r matrix structure for the elliptic calogero moser model in this paper we construct a new lax operator for the elliptic calogero moser model with general from the classical dynamical twisting in which the corresponding r matrix is purely numerical non dynamic the non dynamical r matrix structure of this lax operator is obtained which is the elliptic symmetric r matrix