a diffeomorphism classification of 7 dimensional homogeneous einstein manifolds with mathrm su 3 times mathrm su 2 times mathrm u 1 symmetry on donne des exemples qui montrent que des espaces homogenes homeomorphes ne sont pas necessairement diffeomorphes

homeomorphism classification of positively curved manifolds with almost maximal symmetry rank we show that a closed simply connected 8 manifold 9 manifold of positive sectional curvature on which a 3 torus 4 torus acts isometrically is homeomorphic to a sphere a complex projective space or a quaternionic projective plane sphere we show that a closed simply connected 2m manifold m 5 of positive sectional curvature on which an m 1 torus acts isometrically is homeomorphic to a complex projective space if and only if its euler characteristic is not 2 by wi these results imply a homeomorphism classification for positively curved n manifolds n 8 of almost maximal symmetry rank open image in new window

surgery and duality surgery as developed by browder kervaire milnor novikov sullivan wall and others is a method for comparing homotopy types of topological spaces with difieomorphism or homeomorphism types of manifolds of dimension 5 in this paper a modiflcation of this theory is presented where instead of flxing a homotopy type one considers a weaker information roughly speaking one compares n dimensional compact manifolds with topological spaces whose k skeletons are flxed where k is at least n 2 a particularly attractive example which illustrates the concept is given by complete intersections by the lefschetz hyperplane theorem a complete intersection of complex dimension n has the same n skeleton as n and one can use the modifled theory to obtain information about their difieomorphism type although the homotopy classiflcation is not known the theory reduces this classiflcation result to the determination of complete intersections in a certain bordism group this was under certain restrictions carried out in tr the restrictions are if d d1 dr is the total degree of a complete intersection x n1 dr of complex dimension n then the assumption is that for all primes p with p pi1 n 1 the total degree d is divisible by p 2n 1 2pi1 1 theorem a two complete intersections x n

concavity and rigidity in non negative curvature we show that for a manifold with non negative curvature one obtains a collection of concave functions special cases of which are the concavity of the length of a jacobi field in dimension 2 and the concavity of the volume in general we use these functions to show that there are many cohomogeneity one manifolds which do not carry an analytic invariant metric with non negative curvature this implies in particular that one of the candidates in positively curved cohomogeneity one manifolds and 3 sasakian geometry does not carry an invariant metric with positive curvature

cohomogeneity one topological manifolds revisited we prove a structure theorem for closed topological manifolds of cohomogeneity one this result corrects an oversight in the literature we complete the equivariant classification of closed simply connected cohomogeneity one topological manifolds in dimensions 5 6 and 7 and obtain topological characterizations of these spaces in these dimensions these manifolds are homeomorphic to smooth manifolds

new eigenvalue estimates for complex matrices abstract in a recent work 1 we have proved that all the eigenvalues j of a complex matrix a of order n lie in a disk with center at tr a n and radius n 1 n k 1 n k 2 tr a 2 n 1 2 in this paper we prove that the eigenvalues of a are contained in a rectangle with vertices on the boundary circle of the mentioned disk improving in this way the result in 1 we recall some inequalities which alloww us to bound the radius of the disk and the rectangle the bounds can be computed without knowing the eigenvalues of a

localization of eigenvalues in elliptic regions abstract we prove that the eigenvalues j of an n by n complex matrix a with its characteristic polynomial having real coefficients lie in the elliptic region defined by 2 tr a n 2 2 y 2 2 2 where n 1 n n 1 n re k 2 re te a 2 n 1 2 and n 1 n k 1 n im k 2 1 2 this region is intersected with the strip y 1 2 k 1 u im k 2 1 2 to obtain an improved eigenvalue localization region we also give bounds for the semiaxes which can be computed without knowing the eigenvalues of a when a has r n nonzero eigenvalues we obtain a smaller elliptic region containing such nonzero eigenvalues

stability of the phase motion in race track microtrons we model the phase oscillations of electrons in race track microtrons by means of an area preserving map with a fixed point at the origin which represents the synchronous trajectory of a reference particle in the beam we study the nonlinear stability of the origin in terms of the synchronous phase the phase of the synchronous particle at the injection we estimate the size and shape of the stability domain around the origin whose main connected component is enclosed by an invariant curve we describe the evolution of the stability domain as the synchronous phase varies we also clarify the role of the stable and unstable invariant curves of some hyperbolic fixed or periodic points

eigenvalue estimates for symmetric matrices abstract we use the fact that the set of symmetric positive semidefinite matrices of order n form a cone with a special structure in order to find bounds for the eigenvalues of a symmetric matrix

new conditions for the additive inverse eigenvalue problem for matrices abstract this paper deals with the following inverse eigenvalue problem given an n by n real symmetric matrix a and a set of real numbers i 1 n find a diagonal matrix d such that a d has eigenvalues i for the solvability of this problem a number of necessary conditions and sufficient conditions are known in this work new necessary conditions are derived while some sufficient conditions are optimized in particular one sufficient condition due to morel is obtained by optimizing a sufficient condition discovered by laborde

mel nikov s function for two dimensional mappings this paper calculates explicitly the mel nikov function for general perturbations of two dimensional maps possessing a saddle connection this result may be considered as the discrete analogue of ziglin s calculation of the mel nikov function for time periodic perturbations of two dimensional continuous flows key words integrable planar maps perturbations homoclinic orbits mel nikov s function poisson summation formula

a refined formula for the separatrix splitting for the standard map abstract we study the standard map for small values of a parameter e an asymptotic formula is found which describes the size of the splitting of the stable and unstable separatrices of the origin considered as a hyperbolic fixed point the formula contains an exponentially decreasing expression times an asymptotic series on powers of a small parameter the coefficients in the asymptotic expansion are to be found in the process of solving numerically a nonlinear recurrent system of difference equations in the complex domain

on the topology of positively curved 4 manifolds with symmetry soit m une variete compacte a courbure positive orientable a 4 dimensions si m a un champ de vecteurs de killing non trivial alors m est homeomorphe a s 4 ou cp 2

seven dimensional cohomogeneity one manifolds with nonnegative curvature we show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature unless it admits one with positive curvature as a consequence the classification of nonnegatively curved cohomogeneity one manifolds in dimension seven is reduced to only one further family of candidates

a proof of the exponentially small transversality of the separatrices for the standard map in 1984 v f lazutkin laz84 lst89 obtained an asymptotic formula for the separatrix splitting angle for the standard map the difficulty of this problem is related to the exponential smallness of the splitting with respect to a perturbation parameter lazutkin s proof was based on two conjectures probably the original form of those conjectures was incorrect but lazutkin s method was very efficient and inspired a large number of studies on the exponentially small splitting of separatrices the consequent works laz91 laz92 gls94 and gel96 prepared the base to fill all the gaps of the original proof the present paper contains a complete and self contained proof of a refined version of the original formula formula 1 7 of the present paper in this form the formula was obtained in gls94 the proof is inspired by the ideas of lazutkin s original paper laz84

positively curved manifolds with maximal discrete symmetry rank let m be a closed simply connected n manifold of positive sectional curvature we determine its homeomorphism or homotopic type if m also admits an isometric elementary p group action of large rank our main results are there exists a constant p n 0 such that 1 if m 2 n admits an effective isometric inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i action for a prime p p n then k n and implies that m 2 n is homeomorphic to a sphere or a complex projective space 2 if m 2 n 1 admits an isometric s 1 inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i action for a prime p p n then k n and implies that m is homeomorphic to a sphere 3 for m in 1 or 2 if n 7 and k 3 n 4 2 then m is homeomorphic to a sphere or homotopic to a complex projective space

a decreasing sequence of eigenvalue localization regions abstract we construct a decreasing sequence of rectangles rp in such a way that all the eigenvalues of a complex matrix a are contained in each rectangle when a is a matrix with real spectrum or a normal matrix each rp can be obtained without knowing the eigenvalues of a

splitting of separatrices for standard and semistandard mappings abstract we investigate chirikov s standard mapping which is a model for the onset of nonintegrability in nonlinear hamiltonian systems the asymptotic formula when the deviation from an integrable system is small for the angle of intersection of separatrices at a homoclinic point is derived on the basis of approximation by the green percival semistandard mapping in the complex domain computed data on the splitting of separatrices for the semi standard map are presented from which we derive the pre exponential coefficient in the formula for splitting of separatrices in the standard mapping

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

on stochastic sea of the standard map consider a generic one parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism we show that for many parameters residual subset in an open set approaching the critical value the corresponding diffeomorphism has a transitive invariant set of full hausdorff dimension the set is a topological limit of hyperbolic sets and is accumulated by elliptic islands

perron root bounding for nonnegative persymmetric matrices the eigenvalue problem for a symmetric persymmetric matrix can be reduced to two symmetric eigenvalue problems of lower order in this paper we find in which of these problems the perron root of a nonnegative symmetric persymmetric matrix lies this is applied to bound the perron root of such class of matrices

breathers on diatomic fermi pasta ulam lattices we prove the existence of breathers spatially localized and time periodic oscillations in diatomic fermi pasta ulam fpu chains with arbitrary mass ratio this completes an existence result by livi spicci and mackay valid for large mass ratio the problem is formulated as a mapping in a loop space and analyzed via a discrete spatial centre manifold reduction plane wave solutions of the linearized system have frequencies in a higher optic band or a lower acoustic band for frequencies close to band edges all small amplitude solutions of the nonlinear system lie on a finite dimensional centre manifold which reduces the problem locally to the study of a finite dimensional mapping for good parameter values the map admits homoclinic orbits to 0 corresponding to discrete breathers when the fpu interaction potential satisfies a hardening condition we find breathers with frequencies slightly above the optic band or in the gap slightly above the acoustic band for a potential satisfying the opposite softening condition we obtain breathers with frequencies in the gap slightly below the optic band 2004 elsevier b v all rights reserved

splitting of a small separatrix loop near the saddle center bifurcation in area preserving maps abstract when the saddle center bifurcation occurs in an analytic family of area preserving maps a parabolic fixed point first appears at the origin and then this point bifurcates creating an elliptic fixed point and a hyperbolic one separatrices of the hyperbolic fixed point form a small loop around the elliptic point in general the separatrices intersect transversely and the splitting is exponentially small with respect to the perturbation parameter we derive an asymptotic formula which describes the splitting and study the properties of the pre exponential factor

diffeomorphism type of the berger space so 5 so 3 we compute the eells kuiper invariant of the berger manifold so 5 so 3 and determine that it is diffeomorphic to the total space of an s 3 bundle over s 4 this answers a question raised by k grove and w ziller

curvature and symmetry of milnor spheres since milnor s discovery of exotic spheres mi one of the most intriguing problems in riemannian geometry has been whether there are exotic spheres with positive curvature it is well known that there are exotic spheres that do not even admit metrics with positive scalar curvature hi on the other hand there are many examples of exotic spheres with positive ricci curvature cf ch1 he po and na and this work recently culminated in wr where it is shown that every exotic sphere that bounds a parallelizable manifold has a metric of positive ricci curvature this includes all exotic spheres in dimension 7 so far however no example of an exotic sphere with positive sectional curvature has been found in fact until now only one example of an exotic sphere with nonnegative sectional curvature was known the so called gromoll meyer sphere gm in dimension 7 as one of our main results we prove

new examples of manifolds with strictly positive curvature berger 3 wallach 10 and berard bergery 2 have classified all simply connected smooth manifolds which allow a homogeneous riemannian metric of strictly positive curvature besides the rank one symmetric spaces there exist five exceptional manifolds and an infinite series of 7 manifolds of distinct homotopy type which have been studied by aloft and wallach 1 these are diffeomorphic to mpq su 3 upq where p q are positive integers and upq is the one parameter subgroup of diagonal matrices

kreck stolz invariants for quaternionic line bundles we generalise the kreck stolz invariants s2 and s3 by defining a new invariant the t invariant for quaternionic line bundles over closed spin manifolds m of dimension 4k 1 with h 3 m q h 4 m q 0 the t invariant classifies closed smooth oriented 2 connected rational homology 7 spheres up to almost diffeomorphism and detects exotic homeomorphisms between such manifolds the t invariant also provides information about quaternionic line bundles over a fixed manifold and we use it to give a new proof of a theorem of feder and gitler about the values of the second chern classes of quaternionic line bundles over hp k the t invariant for s 4k 1 is closely related to the adams e invariant on the 4k 5 stem

bounds for the spectral radius and the largest singular value abstract we derive an increasing sequence of lower bounds for the spectral radius of a matrix with real spectrum and progressively improved bounds for the largest singular value of a complex matrix we also find estimates for the rank of normal matrices with real spectrum and for the rank of normal nonnegative matrices including some sufficient condition for such matrices to be invertible

positively curved manifolds with symmetry there are very few examples of riemannian manifolds with positive sectionalcurvature known in fact in dimensions above 24 all known examplesare diffeomorphic to locally rank one symmetric spaces we give a partialexplanation of this phenomenon by showing that a positively curved simplyconnected compact manifold m g is up to homotopy given by a rank onesymmetric space provided that its isometry group iso m g is large moreprecisely we prove first that if dim iso m g i 2 dim m 6 then m is tangentially homotopically equivalent to a rank one symmetric space or m is homogeneous secondly we show that in dimensions above 18 k 1 2 each m is tangentially homotopically equivalent to a rank one symmetric space where k 0 denotes the cohomogeneity k dim m iso m g