adaptive predefined performance control for mimo systems with unknown direction via generalized fuzzy hyperbolic model an adaptive predefined performance control problem is investigated for a class of multiple input multiple output systems with unknown control direction and unknown backlash like hysteresis nonlinearities by using generalized fuzzy hyperbolic model gfhm compared with the existing methods the main features are as follows the prediction error is introduced to construct the adaptive laws which means that the approximate accuracy of the gfhm is solved the nussbaum type gain is utilized to deal with the unknown control direction which avoids the requirement of direction a priori and by transforming the tracking errors into new error variables the prescribed steady state and transient performance can be ensured it is shown that the proposed control approach can guarantee that all the signals of the resulting closed loop systems are bounded and the output tracks a desired trajectory while the tracking errors are confined all times within the prescribed bounds finally two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach since the proposed control strategy is only implemented in a healthy case how to extend the strategy to a faulty case will be a further topic

the weil petersson hessian of length on teichmuller space we present a brief but nearly self contained proof of a formula for the weil petersson hessian of the geodesic length of a closed curve either simple or not simple on a hyperbolic surface the formula is the sum of the integrals of two naturally defined positive functions over the geodesic proving convexity of this functional over teichmuller space due to wolpert 1987 we then estimate this hessian from below in terms of local quantities and distance along the geodesic the formula extends to proper arcs on punctured hyperbolic surfaces and the estimate to laminations wolpert s result that the thurston metric is a multiple of the weil petersson metric directly follows on taking a limit of the formula over an appropriate sequence of curves we give further applications to upper bounds of the hessian especially near pinching loci recover through a geometric argument wolpert s result on the convexity of length to the half power and give a lower bound for growth of length in terms of twist

algebraic convergence of schottky groups a discrete faithful representation of the free group on g generators f g into isom h 3 is said to be a schottky group if h 3 d is homeomorphic to a handlebody h g where d is the domain of discontinuity for s action on the sphere at infinity for h 3 schottky space s g the space of all schottky groups is parameterized by the quotient of the teichmuller space f s g of the closed surface of genus g by mod 0 h g where mod 0 h g is the group of isotopy classes of homeomorphisms of s g which extend to homeomorphisms of h g which are homotopic to the identity masur exhibited a domain o h g of discontinuity for mod 0 h g s action on pl s g the space of projective measured laminations on s g so b h g o h g mod 0 h g may be appended to s g as a boundary

complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

on monodromy of complex projective structures we prove that for any nonelementary representation 1 s sl 2 of the fundamental group of a closed orientable hyperbolic surfaces there exists a complex projective structure ons with the monodromy

uniform bounds for weil petersson curvatures we find bounds for weil petersson holomorphic sectional curvature and the weil petersson curvature operator in several regimes that do not depend on the topology of the underlying surface among other results we show that the minimal weil petersson holomorphic sectional curvature of a sufficiently thick hyperbolic surface is comparable to 1 independently of the genus this provides a counterexample to some suggestions that the weil petersson metric becomes asymptotically flat as the genus g goes to infinity in some loci in teichmuller space adopting a different perspective on curvature we also show that the minimal most negative eigenvalue of the curvature operator at any point in the teichmuller space teich sg of a closed surface sg of genus g is uniformly bounded away from zero restricting to a thick part of teich sg we show that the minimal eigenvalue is uniformly bounded below by an explicit constant which does not depend on the topology of the surface but only on the given bound on injectivity radius

meromorphic quadratic differentials and measured foliations on a riemann surface we describe the space of measured foliations induced on a compact riemann surface by meromorphic quadratic differentials we prove that any such foliation is realized by a unique such differential q if we prescribe in addition the principal parts of sqrt q at the poles this generalizes a theorem of hubbard and masur for holomorphic quadratic differentials the proof analyzes infinite energy harmonic maps from the riemann surface to mathbb r trees of infinite co diameter with prescribed behavior at the poles

cyclic surfaces and hitchin components in rank 2 we prove that given a hitchin representation in a real split rank 2 group g 0 there exists a unique equivariant minimal surface in the corresponding symmetric space as a corollary we obtain a parametrization of the hitchin components by a hermit ian bundle over teichmuller space the proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of g 0 some partial extensions of the construction hold for cyclic bundles in higher rank

adaptive control for uncertain continuous time systems using implicit inversion of prandtl ishlinskii hysteresis representation in this note an implicit inversion approach is introduced to avoid difficulties associated with stability analysis in the direct application of inversion for operator based hysteresis models based on this implicit inversion an adaptive control algorithm is formulated for continuous time linear dynamical systems preceded with hysteresis nonlinearities described by the prandtl ishlinskii model a stability analysis of the controlled system is performed to show that zero output tracking error can be achieved simulation results show the effectiveness of the proposed algorithm

qualitative properties of systems of two complex homogeneous ode s a connection to polygonal billiards a correspondence between the orbits of a system of two complex homogeneous polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed this correspondence is general in the sense that it applies to an open set of systems of ordinary differential equations of the specified kind this allows us to transfer results well known from the theory of polygonal billiards such as ergodicity the existence of periodic orbits the absence of exponential divergence the existence of additional conservation laws and the presence of discontinuities in the dynamics to the corresponding systems of ordinary differential equations it also shows that the considerable intricacy known to exist for polygonal billiards also attends these apparently simpler systems of ordinary differential equations

the boundary of an affine invariant submanifold we study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area abelian differentials over nodal riemann surfaces modulo zero area components the main result is a formula for the tangent space to the boundary we also prove finiteness results concerning cylinders a partial converse to the cylinder deformation theorem and a result generalizing part of the veech dichotomy

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

moduli spaces of higgs bundles on degenerating riemann surfaces abstract we prove a gluing theorem for solutions a 0 0 of hitchin s self duality equations with logarithmic singularities on a rank 2 vector bundle over a noded riemann surface 0 representing a boundary point of teichmuller moduli space we show that every nearby smooth riemann surface 1 carries a smooth solution a 1 1 of the self duality equations which may be viewed as a desingularization of a 0 0

new size curvature conditions for strict quasiconvexity of sets given a closed not necessarily convex set d of a hilbert space the problem of the existence of a neighborhood mathcal v on which the projection on d is uniquely defined and lipschitz continuous is considered and such that the corresponding minimization problem has no local minima after having equipped the set d with a family mathcal p of paths playing for d the role the segments play for a convex set the notion of strict quasiconvexity of d mathcal p is defined which will ensure the existence of such a neighborhood mathcal v two constructive sufficient conditions for the strict quasiconvexity of d are given the r g size times curvature condition and the theta size times curvature condition which both amount to checking for the strict positivity of quantities defined by simple formulas in terms of arc length tangent vectors and radii of curvature along all paths of mathcal p an application to the study of wellposedness and local minima of a nonlinear least

numerical solution of inverse scattering problems with multi experimental limited aperture data in this paper a regularized homotopy continuation method is presented for numerical solution of nonlinear ill posedness inverse problems two major difficulties for solving these inverse problems by an optimization method are the ill posedness and the presence of many local minima classic iterative methods such as gauss newton or levenberg marquardt algorithms offer fast local convergence but might not be able to compute the global minimum based on a natural concept of multi experimental data a regularized homotopy continuation method is constructed to compute the global minimum as the experimental index t increases continuously the global minimizer can be computed continuously by using local optimization methods by discretizing the continuous homotopy method various recursive linearization algorithms are developed these algorithms are applied to numerical solution of an inverse medium scattering problem which reconstructs the refractive index of an inhomogeneous medium from limited aperture measurements of the far field pattern of the scattered fields it is assumed that the data is measured at multiple frequencies the inverse scattering problem with limited aperture is challenging since without full aperture measurements the ill posedness and nonlinearity of the inverse problem become more severe an efficient regularized iterative linearization method recursive linearization with respect to the wave number is developed for solving the inverse problem the convergence of the iterative method is examined by numerical examples

the manifold of compatible almost complex structures and geometric quantization let m be an integral symplectic manifold we study a family of hermitian vector bundles on the space mathcal j of almost complex structures on m compatible with whose fibers consist of nearly holomorphic sections of powers of a prequantum line bundle we obtain asymptotics of the curvature of a natural connection in these bundles these results together with toeplitz operator theory provide another proof of donaldson s result that the action of ham m on mathcal j is hamiltonian with moment map the scalar curvature we also give an example involving teichmuller space and discuss a relationship between parallel transport and the schrodinger equation

billiards in polygons survey of recent results in the ten or so years since the publication of ref 19 polygonal billiards have remained an active subject of research in the mathematics and physics literature as a result our understanding of the subject although still far from being complete is much better than it was ten years ago this survey attempts to give a broad overview of the dynamics of billiards in polygons with an emphasis on the material that was not in the literature in 1985 this is not a survey of the publications on polygonal billiards and we apologize to authors whose work has not been included the selection of topics has been strongly influenced by the personal taste of the author and by space limitations thus we do not discuss quantum polygonal billiards in particular quantum chaos see e g refs 41 44 and 45 we hope that somebody will write a survey on this important subject in the near future a fascinating aspect of the subject is the interplay between the geometric shape of the billiard table i e a planar curve and the qualitative features of the billiard dynamics hence it is instructive to compare polygonal billiard tables with other classes of billiard tables in particular the smooth strictly convex tables and the dispersing or sinai tables produce strikingly different types of billiard dynamics we recommend refs 46 and 15 for a general overview of the subject and a comparative study of billiard dynamics for various types of billiard tables

adaptive variable structure control of a class of nonlinear systems with unknown prandtl ishlinskii hysteresis control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task and has received increasing attention in recent years due to growing industrial demands involving varied applications in the literature many mathematical models have been proposed to describe the hysteresis nonlinearities the challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system the purpose of the note is to show such a possibility by using the prandtl ishlinskii pi hysteresis model an adaptive variable structure control approach serving as an illustration is fused with the pi model without necessarily constructing a hysteresis inverse the global stability of the system and tracking a desired trajectory to a certain precision are achieved simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach

completely periodic directions and orbit closures of many pseudo anosov teichmueller discs in q 1 1 1 1 in this paper we investigate the closure of a large class of teichmuller discs in the stratum mathcal q 1 1 1 1 or equivalently in a rm gl 2 mathbb r invariant locus mathcal l of translation surfaces of genus three we describe a systematic way to prove that the rm gl 2 mathbb r orbit closure of a translation surface in mathcal l is the whole locus mathcal l the strategy of the proof is an analysis of completely periodic directions on such a surface and an iterated application of ratner s theorem to unipotent subgroups acting on an adequate splitting this analysis applies for example to all teichmuller discs obtained by the thurston veech s construction with a trace field of degree three which are moreover obviously not veech we produce an infinite series of such examples and show moreover that the favourable splitting situation does not arise everywhere on mathcal l contrary to the situation in genus two we also study completely periodic directions on translation surfaces in mathcal l for instance we prove that completely periodic directions are dense on surfaces obtained by the thurston veech s construction

regularity of harmonic maps to trees we derive regularity theorems and local finiteness results in this paper we first prove the regularity type theorem for harmonic maps to r trees that is when the order of a harmonic map at a point is sufficiently close to 1 then this point is a regular point we then prove a regularity theorem near higher order points we show that if the image of a fixed ball of a properly normalized harmonic map is sufficiently close to a subtree then the image of a smaller ball of this map lies in that subtree as an application we prove that the local image of a harmonic map to an r tree lies in a finite homogeneous subtree

grafting pruning and the antipodal map on measured laminations grafting a measured lamination on a hyperbolic surface de nes a self map of teichmuller space which is a homeomorphism by a result of scannell and wolf in this paper we study the large scale behavior of pruning which is the inverse of grafting speci cally for each conformal structure x t s pruning x gives a map ml s t s we show that this map extends to the thurston compacti cation of t s and that its boundary values are the natural antipodal involution relative to x on the space of projective measured laminations we use this result to study thurston s grafting coordinates on the space of cp structures on s for each x t s we show that the boundary of the space p x of cp structures on x in the compactication of the grafting coordinates is the graph ix of the antipodal involution ix pml s pml s

minimal graphs over riemannian surfaces and harmonic diffeomorphisms we construct a parabolic entire minimal graph s over a finite topology complete riemannian surface sigma of curvature 1 and infinite area thus of non parabolic conformal type the vertical projection of this graph yields a harmonic diffeomorphism from s onto sigma the proof uses the theory of divergence lines to construct minimal graphs we also generalize a theorem of r schoen let g 1 and g 2 be two complete metrics on a orientable surface s with compact boundary and suppose int s r 2 k g 2 d sigma g 2 le c ln 2 r for some c 0 and all r 0 if there is a harmonic diffeomorphism from s g 1 to s g 2 then s g 1 is parabolic

harmonic degree 1 maps are diffeomorphisms lewy s theorem for curved metrics in 1936 h lewy showed that the jacobian determinant of a harmonic homeomorphism between planar domains does not vanish and thus the map is a diffeomorphism this built on the earlier existence

asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented we consider two possible input nonlinearities that is backlash like hysteresis and symmetric dead zone which can be simultaneously dealt with by using the proposed compensation controllers the knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required only the boundedness of the reference signal is assumed the nussbaum gain approach is employed to remove the assumption on the control gain sign the first scheme is based on the backstepping technique the final step of the recursive design is crucial for the closed loop stability in the second scheme a direct adaptive control law is designed the controller has a simple structure and only one adaptation parameter is updated in both controllers it is shown that asymptotic tracking is ensured two numerical examples are provided to show the effectiveness of the theor

radiation pattern evaluation from near field intensities on planes this paper describes analyzes and implements an approach to far field determination from phaseless measurements over two planar surfaces a proper formulation of the problem is considered as a quadratic inverse one whose data is the square amplitude of the near field a solution is introduced as the global minimum of an appropriate functional next to perform such a minimization procedure a finite dimensional representation of the field radiated by sources whose plane wave spectrum becomes negligible outside a fixed angular domain is used a detailed investigation of the properties of the mapping connecting the unknowns to the data makes it possible to analyze how to escape from the local minima possibly met in the course of the minimization procedure to this end the crucial role of the availability of phaseless data over two different sarfa ces and of appropriate weights in the functional definition is emphasized and a reliable iterative procedure converging on the solution regardless of the starting point is thus obtained this property is confirmed by experimental results concerning near zone data from a shaped reflector at 9 ghz it can be readily appreciated that when only the field intensity is detected the complexity and the cost of the equipment required for near field techniques in antenna testing and diagnostics can be reduced to a very large extent

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

periodic billiard orbits are dense in rational polygons we show that periodic orbits are dense in the phase space for billiards in polygons for which the angle between each pair of sides is a rational multiple of 7r

the grafting map of teichmuller space one of the underlying principles in the study of kleinian groups is that aspects of the complex projective geometry of quotients of by these groups reflect properties of the three dimensional hyperbolic geometry of the quotients ofh by these groups yet even though it has been over thirty five years since lipman bers exhibited a holomorphic embedding of the teichmuller space of riemann surfaces in terms of the projective geometry of a teichmuller space of quasi fuchsian manifolds no corresponding embedding in terms of the three dimensional hyperbolic geometry has been presented one of the goals of this paper is to give such an embedding this embedding is straightforward and has been expected for some time ta97 mc98 to each member of a bers slice of the space qf of quasi fuchsian 3manifolds we associate the bending measured lamination of the convex hull facing the fixed conformal end the geometric relationship between a boundary component of a convex hull and the projective surface at infinity for its end is given by a process known as grafting an operation on projective structures on surfaces that traces its roots back at least to klein kl33 p 230 50 with a modern history developed by many authors ma69 he75 fa83 st83 go87 gkm00 ta97 mc98 the main technical tool in our proof that bending measures give coordinates for bers slices and the second major goal of this paper is the completion of the proof of the grafting conjecture this conjecture states that for a fixed measured lamination the self map of teichmuller space induced by grafting a surface along is a homeomorphism of teichmuller space our contribution to this argument is a proof of the injectivity of the grafting map while the principal application of this result that we give is to geometric coordinates on the bers slice of qf one expects that the grafting homeomorphism might lead to other systems of geometric coordinates for other families of kleinian groups see 5 2 thus we feel that this result is of interest in its own right we now state our results and methods more precisely throughout s will denote a fixed differentiable surface which is closed orientable and of genus g 2 let tg be the corresponding teichmuller space of marked conformal structures on s and let pg denote the deformation space of complex projective structures on s see 2 for definitions

existence of closed geodesics through a regular point on translation surfaces we show that on any translation surface if a regular point is contained in some simple closed geodesic then it is contained in infinitely many simple closed geodesics whose directions are dense in mathbb rp 1 moreover the set of points that are not contained in any simple closed geodesic is finite we also construct explicit examples showing that such points exist on some translation surfaces for a surface in any hyperelliptic component we show that this finite exceptional set is actually empty the proofs of our results use apisa s classifications of periodic points and of text gl 2 mathbb r orbit closures in hyperelliptic components as well as a recent result of eskin filip wright

on periodic billiard trajectories in obtuse triangles in 1775 j f de tuschis a fagnano observed that in every acute triangle the orthoptic triangle represents a periodic billiard trajectory but to the present day it is not known whether or not in every obtuse triangle a periodic billiard trajectory exists the limiting case of right triangles was settled in 1993 by f holt who proved that all right triangles possess periodic trajectories the same result had appeared independently in the russian literature in 1991 namely in the work of g a gal perin a m stepin and y b vorobets the latter authors discovered in 1992 a class of obtuse triangles which contain particular periodic billiard paths in this article we review the above mentioned results and some of the techniques used in the proofs and at the same time show for an extended class of obtuse triangles that they contain periodic billiard trajectories

decentralized adaptive stabilization in the presence of unknown backlash like hysteresis due to the difficulty of handling both hysteresis and interactions between subsystems there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis even though the problem is practical and important in this paper we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach for each subsystem a general transfer function with arbitrary relative degree is considered the interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions in the first scheme no knowledge is assumed on the bounds of unknown system parameters in case that the uncertain parameters are inside known compact sets we propose an alternative scheme where a projection operation is employed in the adaptive laws in both schemes the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws it is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system bounded a root mean square type of bound is obtained for the system states as a function of design parameters this implies that the transient system performance can be adjusted by choosing suitable design parameters with scheme ii the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available in the absence of hysteresis perfect stabilization is ensured and the l 2 norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied

the monodromy groups of schwarzian equations on closed riemann surfaces let 1 r psl 2 be a homomorphism of the fundamental group of an oriented closed surface r of genus exceeding one we will establish the following theorem theorem necessary and sufficient for to be the monodromy representation associated with a complex projective stucture on r either unbranched or with a single branch point of order 2 is that 1 r be nonelementary a branch point is required if and only if the representation does not lift to sl 2

polynomial quadratic differentials on the complex plane and light like polygons in the einstein universe abstract we construct geometrically a homeomorphism between the moduli space of polynomial quadratic differentials on the complex plane and light like polygons in the 2 dimensional einstein universe as an application we find a class of minimal lagrangian maps between ideal polygons in the hyperbolic plane

skinning maps are finite to one we show that thurston s skinning maps of teichmuller space have finite fibers the proof centers around a study of two subvarieties of the rm sl 2 mathbb c character variety of a surface one associated with complex projective structures and the other associated with a 3 manifold using the morgan shalen compactification of the character variety and author s results on holonomy limits of complex projective structures we show that these subvarieties have only a discrete set of intersections

conformal limits and the bialynicki birula stratification of the space of λ connections abstract the bialynicki birula decomposition of the space of connections restricts to the morse stratification on the moduli space of higgs bundles and to the partial oper stratification on the de rham moduli space of holomorphic connections for both the morse and partial oper stratifications every stratum is a holomorphic lagrangian fibration over a component of the space of complex variations of hodge structure in this paper we generalize known results for the hitchin section and the space of opers to arbitrary strata these include the following a biholomorphic identification of the fibers of the two strata over a stable variation of hodge structure via the conformal limit of gaiotto a proof that the fibers of the morse and partial oper stratifications are transverse at the base point and an explicit parametrization of the fibers as half dimensional affine spaces

on the uniqueness of weights in single layer perceptrons in this paper the geometric formulation of the single layer perceptron weight optimization problem previously described by coetzee et al 1993 1996 is combined with results from other researchers on nonconvex set projections to describe sufficient conditions for uniqueness of weight solutions it is shown that the perceptron data surface is pseudoconvex and has infinite folding allowing for the specification of a region of desired vectors having unique projections purely in terms of the local curvature of the data surface no information is therefore required regarding the global curvature or size of the data surface these results in principle allow for a posteriori evaluation of whether a weight solution is unique or globally optimal and for a priori scaling of desired vector values to ensure uniqueness through analysis of the input data the practical applicability of these results from a numerical perspective is evaluated on some carefully chosen examples

robust adaptive control of a class of nonlinear systems with unknown backlash like hysteresis deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation by exploiting solution properties of the differential equation and combining those properties with adaptive control techniques a robust adaptive control algorithm is developed without constructing a hysteresis inverse the new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision simulations performed on a nonlinear system illustrate and clarify the approach

adaptive dynamic surface control for mimo nonlinear time varying systems with prescribed tracking performance in this paper an adaptive dynamic surface control scheme is proposed for a class of multi input multi output mimo nonlinear time varying systems by fusing a bound estimation approach a smooth function and a time varying matrix factorisation the obstacle caused by unknown time varying parameters is circumvented the proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step moreover all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance simulation results are presented to illustrate the effectiveness of the proposed scheme

harmonic maps between surfaces and teichmuller spaces we study harmonic maps between two distinct compact riemann surfaces of the same genus our aim is to examine the role of the curvature in the relationship between energies of harmonic maps and conformal metrics on the target surface we consider the energy of the energy minimizing map between the surfaces as a function of the metrics within the conformal class of the target and solve the variational problem of minimizing this functional when we restrict the upper curvature bound and normalize the area of the metrics in doing so we show that the upper curvature bound on the normalized target metric is an obstruction in obtaining a degree 1 conformal harmonic map between distinct riemann surfaces

ergodicity of billiard flows and quadratic differentials on considere un systeme billard de 2 objets de masses m 1 et m 2 on montre que pour un ensemble dense de paires m 1 m 2 ce systeme est ergodique

closed trajectories for quadratic differentials with an application to billiards on considere les orbites periodiques pour le systeme dynamique d une table polygonale avec des angles multiples rationnels de le billard rationnel

stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash like hysteresis this paper deals with adaptive control of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is described by a dynamic equation by utilizing this dynamic model and by combining a fuzzy universal function approximator with adaptive control techniques a stable adaptive fuzzy control algorithm is developed without constructing a hysteresis inverse the stability of the closed loop system is shown using lyapunov arguments the effectiveness of the proposed method is demonstrated through simulations

length spectra and degeneration of flat metrics in this paper we consider flat metrics semi translation structures on surfaces of finite type there are two main results the first is a complete description of when a set of simple closed curves is spectrally rigid that is when the length vector determines a metric among the class of flat metrics secondly we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics the geometric interpretation is that flat metrics degenerate to mixed structures on the surface part flat metric and part measured foliation

adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash like hysteresis in this note we consider the same class of systems as in a previous paper i e a class of uncertain dynamic nonlinear systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation in the presence of bounded external disturbances by using backstepping technique robust adaptive backstepping control algorithms are developed unlike some existing control schemes for systems with hysteresis the developed backstepping controllers do not require the uncertain parameters within known intervals also no knowledge is assumed on the bound of the disturbance like term a combination of the external disturbances and a term separated from the hysteresis model it is shown that the proposed controllers not only can guarantee global stability but also transient performance

brief paper adaptive tracking of nonlinear systems with non symmetric dead zone input quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead zone nonlinearities however adaptive tracking of systems with non symmetric dead zone characteristics has not been fully discussed with minimal knowledge of the dead zone parameters it is shown that the controlled system preceded by a non symmetric dead zone input can be represented as an uncertain nonlinear system subject to a linear input with time varying input coefficient to cope with this problem a new adaptive compensation algorithm is employed without constructing the dead zone inverse the proposed adaptive scheme requires only the information of bounds of the dead zone slopes and treats the time varying input coefficient as a system uncertainty the new control scheme ensures bounded error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop by appropriate selections of the controller parameters we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control a numerical example is included to show the effectiveness of the theoretical results

holonomy limits of complex projective structures abstract we study the limits of holonomy representations of complex projective structures on a compact riemann surface in the morgan shalen compactification of the character variety we show that the dual r trees of the quadratic differentials associated to a divergent sequence of projective structures determine the morgan shalen limit points up to a natural folding operation for quadratic differentials with simple zeros no folding is possible and the limit of holonomy representations is isometric to the dual tree we also derive an estimate for the growth rate of the holonomy map in terms of a norm on the space of quadratic differentials

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach