towards a finite presentation for the nottingham group this paper exhibits 2 generators for the nottingham group n fp for p 3 and p 52 relations that they satisfy modulo terms of the lower central series and begins an investigation of the properties of an infinite pro p group g with a pair of generators satisfying these relations the ultimate aim is to show that the graded lie algebras of g and n fp with respect to their lower central series are isomorphic

automorphisms of the nottingham group abstract let k be a finite field of characteristic p 5 the nottingham group n over k is the group of normalised automorphisms of the local field k t in this paper we determine the automorphism group of n in particular we show that every automorphism of the nottingham group is standard we also give a complete description of the conjugacy classes of elements of order p in n

hausdorff dimension pro p groups and kac moody algebras every finitely generated profinite group can be given the structure of a metric space and as such it has a well defined hausdorff dimension function in this paper we study hausdorff dimension of closed subgroups of finitely generated pro p groups g we prove that if g is p adic analytic and h c g is a closed subgroup then the hausdorff dimension of h is dimh dimg where the dimensions are of h and g as lie groups letting the spectrum spec g of g denote the set of hausdorff dimensions of closed subgroups of g it follows that the spectrum of p adic analytic groups is finite and consists of rational numbers we then consider some non p adic analytic groups g and study their spectrum in particular we investigate the maximal hausdorff dimension of nonopen subgroups of g and show that it is equal to 1 1 d 1 in the case of g sld fp t where p 2 and to 1 2 if g is the so called nottingham group where p 5 we also determine the spectrum of sl2 fp t p 2 completely showing that it is equal to 0 2 3 1 some of the proofs rely on the description of maximal graded subalgebras of kac moody algebras recently obtained by the authors in joint work with e i zelmanov

levi flat hypersurfaces with real analytic boundary let x be a stein manifold of dimension at least 3 given a compact codimension 2 real analytic submanifold m of x that is the boundary of a compact levi flat hypersurface h we study the regularity of h suppose that the cr singularities of m are an o x convex set for example suppose m has only finitely many cr singularities which is a generic condition then h must in fact be a real analytic submanifold if m is real algebraic it follows that h is real algebraic and in fact extends past m even near cr singularities to prove these results we provide two variations on a theorem of malgrange that a smooth submanifold contained in a real analytic subvariety of the same dimension is itself real analytic we prove a similar theorem for submanifolds with boundary and another one for subanalytic sets

normal forms for nonintegrable almost cr structures we propose two constructions extending the chern moser normal form to non integrable levi nondegenerate hypersurface type almost cr structures one of them translates the chern moser normalization into pure intrinsic setting whereas the other directly extends the extrinsic chern moser normal form by allowing non cr embeddings that are in some sense maximally cr one of the main differences with the classical integrable case is the presence of the non integrability tensor at the same order as the levi form making impossible a good quadric approximation a key tool in the chern moser theory partial normal forms are obtained for general almost cr structures of any cr codimension in particular for almost complex structures applications are given to the equivalence problem and the lie group structure of the group of all cr diffeomorphisms

analytical and numerical stability of neutral delay integro differential equations and neutral delay partial differential equations this paper is concerned with the analytical and numerical stability of neutral delay integro differential equations ndides and neutral delay partial differential equations ndpdes we study the delay dependent stability of the real coefficient linear test equations for ndides furthermore we prove that the trapezium rule can preserve the delay dependent stability of the test equations considered we also discuss the delay dependent stability of the continuous problems the semi discrete problems and the fully discrete problems of linear ndpdes some numerical experiments are given to confirm the theoretical results

stochastic climate dynamics random attractors and time dependent invariant measures a b s t r a c t this article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s the nonlinear deterministic and the linear stochastic one this unification via the theory of random dynamical systems rds allows one to consider the detailed geometric structure of the random attractors associated with nonlinear stochastically perturbed systems we report on high resolution numerical studies of two idealized models of fundamental interest for climate dynamics the first of the two is a stochastically forced version of the classical lorenz model the second one is a low dimensional nonlinear stochastic model of the el nino southern oscillation enso these studies provide a good approximation of the two models global random attractors as well as of the time dependent invariant measures supported by these attractors the latter are shown to have an intuitive physical interpretation as random versions of sinai ruelle bowen srb measures

on the smoothing property of linear delay partial differential equations abstract we consider linear partial differential equations with an additional delay term which under spatial discretization lead to ordinary differential equations with fixed delay of retarded type this means that the semi discrete solution gains smoothness over time for the concept of classical mild and weak solutions we analyse whether this effect also takes place in the original system we show that some systems behave in a neutral way only as a result the smoothness of the exact solution remains unchanged instead of gaining smoothness over time

parameter estimation for energy balance models with memory we study parameter estimation for one dimensional energy balance models with memory ebmms given localized and noisy temperature measurements our results apply to a wide range of nonlinear parab

on an n manifold in mathbf c n near an elliptic complex tangent in this paper we will be concerned with the local biholomorphic properties of a real n manifold m in c at a generic point such a manifold basically has the nature of the standard r in c near a complex tangent however the consideration can be much more complicated and the manifold may acquire a nontrivial local hull of holomorphy and many other biholomorphic invariants the study of such a problem was first carried out in a celebrated paper of e bishop bis where for each sufficiently non degenerate complex tangent he attached a biholomorphic invariant called the bishop invariant when the complex tangent is elliptic i e when 0 12 for a more precise definition see 2 he showed the existence of families of complex analytic disks with boundary on m that shrink down to the locus of points in m with complex tangents in particular using the well known continuity principle one sees that the image m of such families is contained in the holomorphic hull of the manifold at the time he asked whether m gives precisely the local holomorphic hull of m as well as certain uniqueness properties of the attached disks he also proposed the problem of determining the fine structure of m near such complex tangents later there appeared a sequence of papers concerning the smooth character of m in case m c here we would like to mention in particular the famous theorem proved by kenig webster in their deep work kw1 which states that the local hull of holomorphy m near an elliptic complex tangent is a smooth levi flat hypersurface with m c as part of its smooth boundary in another important paper of moser webster mw a systematic normal form theory was employed for the understanding of the local biholomorphic invariants of m in case m is real analytic when the bishop invariant 6 0 their method works in any dimension and even for some hyperbolic complex tangents but it breaks down for complex tangents with 0 among other things they showed that m can be biholomorphically mapped into the affine space

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

automorphisms of harbater katz gabber curves let k be a perfect field of characteristic p 0 and let g be a finite group we consider the pointed g curves over k associated by harbater katz and gabber to faithful actions of g on k t over k we use such hkg g curves to classify the automorphisms of k t of p power order that can be expressed by particularly explicit formulas namely those mapping t to a power series lying in a mathbb z p mathbb z artin schreier extension of k t in addition we give necessary and sufficient criteria to decide when an hkg g curve with an action of a larger finite group j is also an hkg j curve

an energy balance climate model with hysteresis abstract energy balance climate models of budyko type lead to reaction diffusion equations with slow diffusion and memory on the 2 sphere the reaction part exhibits a jump discontinuity at the snow line here we introduce a babuska duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode

transition to turbulence small disturbances and sensitivity analysis i a motivating problem abstract for over 100 years researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized navier stokes equations however for many simple flows this approach fails to match experimental results recently new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system these new mostly linear theories have increased our understanding of the transition process but the role of nonlinearity has not been explored in detail this paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence in this part we study a highly sensitive one dimensional burgers equation as a motivating problem sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance also sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem in the second part of this work this analysis will be extended to the three dimensional navier stokes equations to show that small disturbances have great potential to trigger transition to turbulence

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

embedding properties of hereditarily just infinite profinite wreath products abstract we study infinitely iterated wreath products of finite permutation groups w r t product actions in particular we prove that for every non empty class of finite simple groups x there exists a finitely generated hereditarily just infinite profinite group w with composition factors in x such that any countably based profinite group with composition factors in x can be embedded into w additionally we investigate when infinitely iterated wreath products of finite simple groups w r t product actions are co hopfian or non co hopfian

presenting the graded lie algebra associated to the nottingham group abstract the graded lie algebra l associated to the nottingham group is a loop algebra of the witt algebra w 1 the universal covering w 1 of w 1 has one dimensional centre so that the corresponding loop algebra m of w 1 has an infinite dimensional centre z m as m z m is isomorphic to l it follows from a result of b h neumann that l is not finitely presented however we are able to show that m itself is finitely presented we work more generally with the zassenhaus algebras w n in the group context examples of finitely presented groups whose centre is not finitely generated were given by v n remeslennikov and h abels

a normal form for a real 2 codimensional submanifold in cn 1 near a cr singularity abstract we construct a formal normal form for a class of real submanifolds m c n 1 of codimension 2 near a cr singularity approximating the sphere our result gives a generalization of huang yin s normal form in c 2 to the higher dimensional analog case

flattening of cr singular points and analyticity of the local hull of holomorphy ii abstract this is the second article of the two papers in which we investigate the holomorphic and formal flattening problem of a non degenerate cr singular point of a codimension two real submanifold in c n with n 3 the problem is motivated from the study of the complex plateau problem that looks for the levi flat hypersurface bounded by a given real submanifold and by the classical complex analysis problem of finding the local hull of holomorphy of a real submanifold in a complex space the present article is focused on non degenerate flat cr singular points with at least one non parabolic bishop invariant we will solve the formal flattening problem in this setting the results in this paper and those in 23 are taken from our earlier arxiv post 22 we split 22 into two independent articles to avoid it being too long

abstract commensurators of profinite groups in this paper we initiate a systematic study of the abstract com mensurators of profinite groups the abstract commensurator of a profinite group g is a group comm g which depends only on the commensurability class of g we study various properties of comm g in particular we find two natural ways to turn it into a topological group we also use comm g to study topological groups which contain g as an open subgroup all such groups are totally disconnected and locally compact for instance we con struct a topologically simple group which contains the pro 2 completion of the grigorchuk group as an open subgroup on the other hand we show that some profinite groups cannot be embedded as open subgroups of compactly generated topologically simple groups several celebrated rigidity theorems like pink s analogue of mostow s strong rigidity theorem for simple algebraic groups defined over local fields and the neukirch uchida theorem can be re formulated as structure theorems for the commensurators of certain profinite groups

pseudospectra of the orr sommerfeld operator this paper investigates the pseudospectra and the numerical range of the orr sommerfeld operator for plane poiseuille flow a number z in bf c is in the epsilon pseudospectrum of a matrix or operator a if zi a 1 geq epsilon 1 or equivalently if z is in the spectrum of a e for some perturbation e satisfying e leq epsilon the numerical range of a is the set of numbers of the form au u where cdot cdot is the inner product and u is a vector or function with huh u 1 the spectrum of the orr sommerfeld operator consists of three branches it is shown that the eigenvalues at the intersection of the branches are highly sensitive to perturbations and that the sensitivity increases dramatically with the reynolds number the associated eigenfunctions are nearly linearly dependent even though they form a complete set to understand the high sensitivity of the eigenvalues a model operator is considered related to the airy equation tha

the nottingham group for p 2 abstract in this paper i consider the nottingham group over a finite field of characteristic 2 i obtain a number of results previously known only for nottingham groups in odd characteristic for example i obtain information on the derived series and i prove that the nottingham group is hereditarily just infinite as a pro 2 group as a consequence the nottingham group over any finite field of characteristic 2 is not analytic over any pro 2 ring

convergent normal form and canonical connection for hypersurfaces of finite type in c2 abstract we study the holomorphic equivalence problem for finite type hypersurfaces in c 2 we discover a geometric condition which is sufficient for the existence of a natural convergent normal form for a finite type hypersurface we also provide an explicit construction of such a normal form as an application we construct a canonical connection for a large class of finite type hypersurfaces to the best of our knowledge this gives the first construction of an invariant connection for levi degenerate hypersurfaces in c 2

data driven non markovian closure models abstract this paper has two interrelated foci i obtaining stable and efficient data driven closure models by using a multivariate time series of partial observations from a large dimensional system and ii comparing these closure models with the optimal closures predicted by the mori zwanzig mz formalism of statistical physics multilayer stochastic models msms are introduced as both a generalization and a time continuous limit of existing multilevel regression based approaches to closure in a data driven setting these approaches include empirical model reduction emr as well as more recent multi layer modeling it is shown that the multilayer structure of msms can provide a natural markov approximation to the generalized langevin equation gle of the mz formalism a simple correlation based stopping criterion for an emr msm model is derived to assess how well it approximates the gle solution sufficient conditions are derived on the structure of the nonlinear cross interactions between the constitutive layers of a given msm to guarantee the existence of a global random attractor this existence ensures that no blow up can occur for a broad class of msm applications a class that includes non polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants the emr msm methodology is first applied to a conceptual nonlinear stochastic climate model of coupled slow and fast variables in which only slow variables are observed it is shown that the resulting closure model with energy conserving nonlinearities efficiently captures the main statistical features of the slow variables even when there is no formal scale separation and the fast variables are quite energetic second an msm is shown to successfully reproduce the statistics of a partially observed generalized lotka volterra model of population dynamics in its chaotic regime the challenges here include the rarity of strange attractors in the model s parameter space and the existence of multiple attractor basins with fractal boundaries the positivity constraint on the solutions components replaces here the quadratic energy preserving constraint of fluid flow problems and it successfully prevents blow up

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

the numerical solution of delay differential algebraic equations of retarded and neutral type in this paper we consider the numerical solution of initial value delay differential algebraic equations ddaes of retarded and neutral types with a structure corresponding to that of hessenberg daes we give conditions under which the ddae is well conditioned and show how the ddae is related to an underlying retarded or neutral delay ordinary differential equation dode we present convergence results for linear multistep and runge kutta methods applied to ddaes of index 1 and 2 and show how higher index hessenberg ddaes can be formulated in as stable a way as index 2 hessenberg ddaes we also comment on some practical aspects of the numerical solution of these problems

s shaped bifurcation branch in a quasilinear multivalued model arising in climatology abstract in this paper we show the existence of a continuous and unbounded connected s shaped set q u where q is the solar constant and u satisfies a quasilinear eventually multivalued stationary equation on a riemannian manifold without boundary arising as a stationary energy balance model for the earth surface temperature

new just infinite pro p groups of finite width and subgroups of the nottingham group we use the action of the nottingham group on the completion of its lie algebra to construct new examples of just infinite pro p groups of finite width whose graded lie algebras with respect to the lower central series are isomorphic to sl2 fp tfp t the groups constructed are non linear and thus answer the question posed in comm algebra 30 2002 1293 the proof of nonlinearity uses a new description of the centralizers of elements of order p in the nottingham group and the concept of hausdorff dimension

on lifting commutative dynamical systems we construct a lifting of commuting power series from a residue field of positive characteristic to a local ring in a manner similar to the formal group cohomologies of lubin tate this lifting is then used to prove that a nontorsion zp automorphism and a multiplication by p endomorphism uniquely define a formal group over fields of a positive characteristic this suggests that a characteristic 0 conjecture by lubin could be approached with residue field considerations

finite type hypersurfaces with divergent normal form we consider the convergence problem for normal forms on finite type hypersurfaces in dimension two constructed in kola math res lett 12 897 910 2005 two families of examples of hypersurfaces with divergent normal form are given the results also show that the divergence phenomenon cannot be avoided by a modification of the normal form construction

real submanifolds of maximum complex tangent space at a cr singular point i we study a germ of real analytic n dimensional submanifold of mathbf c n that has a complex tangent space of maximal dimension at a cr singularity under some assumptions we show its equivalence to a normal form under a local biholomorphism at the singularity we also show that if a real submanifold is formally equivalent to a quadric it is actually holomorphically equivalent to it if a small divisors condition is satisfied finally we investigate the existence of a complex submanifold of positive dimension in mathbf c n that intersects a real submanifold along two totally and real analytic submanifolds that intersect transversally at a possibly non isolated cr singularity

index subgroups of the nottingham group abstract it is known that every countably based pro p group embeds as a closed subgroup into the nottingham group j j f p at the same time the subgroup structure of j remains rather mysterious in this paper we introduce the class of so called index subgroups of j and study their fundamental properties two main applications are given i we prove that a certain infinite subclass of index subgroups provides new examples of hereditarily just infinite pro p groups of finite width ii we determine which hausdorff dimensions occur for index subgroups and subsequently show that the hausdorff spectrum of j begins with a proper interval

some hereditarily just infinite subgroups of j abstract this work examines the commutator structure of some closed subgroups of the wild group of automorphisms of a local field with perfect residue field a group we call j in particular we establish a new approach to evaluating commutators in j and using this method investigate the normal subgroup structure of some classes of index subgroups of j as introduced by klopsch we provide new proofs of fesenko s results that lead to a proof that the torsion free group t t k 1 a k t qk 1 a k f p is hereditarily just infinite and by extending his work we also demonstrate the existence of a new class of hereditarily just infinite subgroups of j which have non trivial torsion

global existence and asymptotic behavior for a quasilinear reaction diffusion system from climate modeling abstract this paper is concerned with a weakly coupled system of quasilinear autonomous strongly parabolic equations on a compact two dimensional manifold without boundary the system arises from an energy balance climate model we establish l hoelder and sobolev estimates and apply general results on quasilinear evolution equations in order to guarantee the existence of classical nonnegative solutions more precisely it is shown that the system generates a global solution semiflow in the positive cone of some fractional order sobolev space employing elements of the theory of infinite dimensional dissipative systems we prove the existence of a connected global attractor finally we present some results about stationary solutions and forced periodic oscillations the present paper extends earlier work of the authors on a semilinear problem

normal subgroups in substitution groups of formal power series let r be a commutative ring with 1 and let n r t t2r t be the group of normalized formal power series over r under substitution in this paper we investigate the connection between the ideal structure of r and the normal subgroup structure of n r in particular we show that if k is a finite field of characteristic not equal to two then every proper quotient group of the so called nottingham group n k is finite as a further application we consider the profinite completion of the group n r we show that if every additive subgroup of finite index in r contains an ideal of finite index in r then n r n r

a cohomological treatise of hkg covers with applications to the nottingham group abstract we characterize harbater katz gabber curves in terms of a family of cohomology classes satisfying a compatibility condition our construction is applied to the description of finite subgroups of the nottingham group

semigroups and linear partial differential equations with delay abstract we prove the equivalence of the well posedness of a partial differential equation with delay and an associated abstract cauchy problem this is used to derive sufficient conditions for well posedness exponential stability and norm continuity of the solutions applications to a reaction diffusion equation with delay are given

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given

a bishop surface with a vanishing bishop invariant we give a solution to the equivalence problem for bishop surfaces with the bishop invariant 0 as a consequence we answer in the negative a problem that moser asked in 1985 after his work with webster in 1983 and his own work in 1985 this will be done in two major steps we first derive the formal normal form for such surfaces we then show that two real analytic bishop surfaces with 0 are holomorphically equivalent if and only if they have the same formal normal form up to a trivial rotation our normal form is constructed by an induction procedure through a completely new weighting system from what is used in the literature our convergence proof is done through a new hyperbolic geometry associated with the surface

navier stokes equations with delays some results on the existence and uniqueness of solutions to navier stokes equations when the external force contains some hereditary characteristics are proved