affine actions on lie groups and post lie algebra structures abstract we introduce post lie algebra structures on pairs of lie algebras g n defined on a fixed vector space v special cases are lr structures and pre lie algebra structures on lie algebras we show that post lie algebra structures naturally arise in the study of nil affine actions on nilpotent lie groups we obtain several results on the existence of post lie algebra structures in terms of the algebraic structure of the two lie algebras g and n one result is for example that if there exists a post lie algebra structure on g n where g is nilpotent then n must be solvable furthermore special cases and examples are given this includes a classification of all complex two dimensional post lie algebras

discrete breathers in a two dimensional fermi pasta ulam lattice using asymptotic methods we investigate whether discrete breathers are supported by a two dimensional fermi pasta ulam lattice a scalar one component two dimensional fermi pasta ulam lattice is shown to model the charge stored within an electrical transmission lattice a third order multiple scale analysis in the semi discrete limit fails since at this order the lattice equations reduce to the 2 1 dimensional cubic nonlinear schrodinger nls equation which does not support stable soliton solutions for the breather envelope we therefore extend the analysis to higher order and find a generalised 2 1 dimensional nls equation which incorporates higher order dispersive and nonlinear terms as perturbations we find an ellipticity criterion for the wave numbers of the carrier wave numerical simulations suggest that both stationary and moving breathers are supported by the system calculations of the energy show the expected threshold behaviour whereby the energy of breathers does em not go to zero with the amplitude we find that the energy threshold is maximised by stationary breathers and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

stability of low dimensional bushes of vibrational modes in the fermi pasta ulam chains bushes of normal modes represent the exact excitations in the nonlinear physical systems with discrete symmetries physica d 117 1998 43 the present paper is the continuation of our previous paper physica d 166 2002 208 where these dynamical objects of new type were discussed for the monoatomic nonlinear chains here we develop a simple crystallographic method for finding bushes in nonlinear chains and investigate stability of one and two dimensional vibrational bushes for both fpu and fpu models in particular of those revealed recently in physica d 175 2003 31

tangent bifurcation of band edge plane waves dynamical symmetry breaking and vibrational localization abstract we study tangent bifurcation of band edge plane waves in nonlinear hamiltonian lattices the lattice is translationally invariant we argue for the breaking of permutational symmetry by the new bifurcated periodic orbits the case of two coupled oscillators is considered as an example for the perturbation analysis where the symmetry breaking can be traced using poincare maps next we consider a lattice and derive the dependence of the bifurcation energy on the parameters of the hamiltonian function in the limit of large system sizes a necessary condition for the occurence of the bifurcation is the repelling of the band edge plane wave from the linear spectrum with increasing energy we conclude that the bifurcated orbits will consequently exponentially localize in the configurational space

stochastic model of the width function a new class of probabilistic models of the width function based on so called iterated random pulse irp processes is proposed irp processes reproduce the main characteristics of empirical width functions nonnegativity nonstationarity and power law decay of the spectrum and require few and easily accessible parameters irp models are based on a simple conceptualization of the geometrical structure of river basins and exploit in a natural way the self similarity of natural channel networks a result that is derived from the irp representation is that the exponent of hack s law l a and the exponent of the power spectral density of the width function s are related as 1 empirical values of are typically in the range 1 8 2 0 and are consistent with this theoretical result and the usual range of

the five dimensional complete left symmetric algebra structures compatible with an abelian lie algebra structure abstract the classification of five dimensional complete left symmetric algebras is known to be a hard problem in this paper we establish an explicit classification of the five dimensional complete left symmetric algebras over r having an abelian associated lie algebra a detailed list of all possible isomorphism types is presented

translations in simply transitive affine actions of heisenberg type lie groups let g be a 2 step nilpotent lie group with a 1 dimensional commutator subgroup we prove that for any simply transitive and affine action of g there exists a non trivial subgroup of g acting as pure translations this result no longer holds in case the commutator subgroup is higher dimensional

the classification of novikov algebras in low dimensions novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus for further our understanding and physical applications we give a classification of novikov algebras in dimensions two and three in this paper

post lie algebra structures on pairs of lie algebras abstract we study post lie algebra structures on pairs of lie algebras g n which describe simply transitive nil affine actions of lie groups we prove existence results for such structures depending on the interplay of the algebraic structures of g and n we consider the classes of simple semisimple reductive perfect solvable nilpotent abelian and unimodular lie algebras furthermore we consider commutative post lie algebra structures on perfect lie algebras using lie algebra cohomology we can classify such structures in several cases we also study commutative structures on low dimensional lie algebras and on nilpotent lie algebras

left symmetric algebras from linear functions abstract in this paper some left symmetric algebras are constructed from linear functions they include a kind of simple left symmetric algebras and some examples appearing in mathematical physics their complete classification is also given which shows that they can be regarded as generalization of certain two dimensional left symmetric algebras

on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus they are a class of left symmetric algebras with commutative right multiplication operators which can be viewed as bosonic fermionic novikov algebras are a class of left symmetric algebras with anti commutative right multiplication operators they correspond to a certain hamiltonian superoperator in a supervariable in this paper we commence a study on fermionic novikov algebras from the algebraic point of view we will show that any fermionic novikov algebra in dimension 3 must be bosonic moreover we give the classification of real fermionic novikov algebras on four dimensional nilpotent lie algebras and some examples in higher dimensions as a corollary we obtain kinds of four dimensional real fermionic novikov algebras which are not bosonic all of these examples will serve as a guide for further development including the application in physics

bushes of vibrational modes for fermi pasta ulam chains abstract some exact solutions and multimode invariant submanifolds were found for the fermi pasta ulam fpu model by poggi and ruffo physica d 103 1997 251 in the present paper we demonstrate how results of such a type can be obtained for an arbitrary n particle chain with periodic boundary conditions with the aid of our group theoretical approach physica d 117 1998 43 based on the concept of bushes of normal modes in mechanical systems with discrete symmetry the integro differential equation describing the fpu dynamics in the modal space is derived the loss of stability of the bushes of modes for the fpu model in particular for the limiting case n for the dynamical regime with displacement pattern having period twice the lattice spacing mode is studied our results for the fpu chain are compared with those by poggi and ruffo for the fpu chain

q breathers in fermi pasta ulam chains existence localization and stability the fermi pasta ulam fpu problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model in the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q we continue normal modes from the harmonic limit into the fpu parameter regime and obtain persistence of these periodic orbits termed here q breathers qb they are characterized by time periodicity exponential localization in the q space of normal modes and linear stability up to a size dependent threshold amplitude trajectories computed in the original fpu setting are perturbations around these exact qb solutions the qb concept is applicable to other nonlinear lattices as well

stability of nonlinear modes and chaotic properties of 1d fermi pasta ulam lattices abstract the stability properties of certain simple periodic solutions nonlinear modes of the equations of motion of one dimensional n particle fpu lattices are obtained analytically by uncoupling the n linear variational equations the energy per particle e c n at which these modes first become unstable is calculated and its asymptotic behavior as n is determined we find that for lattices which experience strong energy sharing e c n 0 as n while for a lattice where little energy sharing is observed e c n const 0 as n increases certain possible connections between our local stability results and some global chaotic properties of fpu lattices are discussed

left symmetric algebra structures on the w algebra w 2 2 we study the compatible left symmetric algebra structures on the w algebra w 2 2 with some natural grading conditions the results of earlier work on left symmetric algebra structures on the virasoro algebra play an essential role in determining these compatible structures as a corollary any such left symmetric algebra contains an infinite dimensional trivial subalgebra that is also a submodule of the regular module

relation between grid channel and peano networks in high resolution digital elevation models the topological interconnection between grid channel and peano networks is investigated by extracting grid and channel networks from high resolution digital elevation models of real drainage basins and by using a perturbed form of the equation describing how the average junction degree varies with horton strahler order in peano networks the perturbed equation is used to fit the data observed over the hortonian substructures of real networks the perturbation parameter denoted as uniformity factor is shown to indicate the degree of topological similarity between hortonian and peano networks the sensitivities of computed uniformity factors and drainage densities to grid cell size and selected threshold for channel initiation are evaluated while the topological relation between real and peano networks may not vary significantly with grid cell size these networks are found to exhibit the same drainage density only for specific grid cell sizes which may depend on the selected threshold for channel initiation

nonpersistence of breather families for the perturbed sine gordon equation we show that up to one exception and as a consequence of first order perturbation theory only it is impossible that a large portion of the well known family of breather solutions to the sine gordon equation could persist under any nontrivial perturbation of the form u tt u xx sin u varepsilon delta left u right o left varepsilon 2 right where is an analytic function in anarbitrarily small neighbourhood ofu 0 improving known results we analyze and overcome the particular difficulties that arise when one allows the domain of analyticity of to be small the single exception is a one dimensional linear space of perturbation functions under which the full family of breathers does persist up to first order in e

commutative post lie algebra structures and linear equations for nilpotent lie algebras abstract we show that for a given nilpotent lie algebra g with z g g g all commutative post lie algebra structures or cpa structures on g are complete this means that all left and all right multiplication operators in the algebra are nilpotent then we study cpa structures on free nilpotent lie algebras f g c and discover a strong relationship to solving systems of linear equations of type x u y v 0 for generator pairs x y f g c we use results of remeslennikov and stohr concerning these equations to prove that for certain g and c the free nilpotent lie algebra f g c has only central cpa structures

affine manifolds and orbits of algebraic groups this paper is the sequel to the radiance obstruction and parallel forms on a ffne manifolds lyans amer math soc 286 1984 629 649 which introduced a new family of secondary characteristic classes for affine structures on manifolds the present paper utilizes the representation of these classes in lie algebra cohomology and algebraic group cohomology to deduce new results relating the geometric properties of a compact affine manifold mn to the action on rn of the algebraic hull a r of the affine holonomy group r c aff rn a main technical result of the paper is that if m has a nonzero cohomology class represented by a parallel k form then every orbit of a r has dimension k when m is compact then a r acts transitively provided that m is complete or has parallel volume the converse holds when r is nilpotent a 4 dimensional subgroup of aff r3 is exhibited which does not contain the holonomy group of any compact affine 3 manifold when m has solvable holonomy and is complete then m must have parallel volume conversely if m has parallel volume and is of the homotopy type of a solvmanifold then m is complete if m is a compact homogeneous affine manifold or if m possesses a rational riemannian metric then it is shown that the conditions of parallel volume and completeness are equivalent this paper is the sequel to our previous paper 22 in that paper we exploited certain characteristic classes exterior powers of the radiance obstruction to obtain relationships between various properties of affine manifolds our results supported the conjecture first made by l markus 36 that a compact affine manifold is complete if and only if it has parallel volume we shall refer to this as the main conjecture let m be a compact affine manifold with developing map dev m e and affine holonomy representation h 7r h 7r r c aff e here 1r is the group of deck transformations of the universal cover m e is the vector space rn and aff e is the group of affine automorphisms of e the map dev is a locally affine immersion which is equivariant respecting h the linear holonomy homb morphism is the composition a 1r gl e of h with the natural homomorphism l aff e gl e the obstruction to r fixing a point in e is a 1 dimensional cohomology class cm e h1 m ex with coefficients in e twisted by a it comes from a universal class in the group cohomology h1 aff e el which contains the crossed homomorphism u aff e e g g 0 received by the editors december 12 1984 and in revised form may 29 1985 1980 mathematics subject classification 1985 revision primary 57r99 53c05 secondary 53c10 55r25 1 research partially supported by fellowships and grants from the national science foundation a 1986 american mathematical society 0002 9947 86 1 00 25 per page

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

isochronism and tangent bifurcation of band edge modes in hamiltonian lattices abstract in physica d s flach physica d 91 1996 223 results were obtained regarding the tangent bifurcation of the band edge modes q 0 of nonlinear hamiltonian lattices made of n coupled identical oscillators introducing the concept of partial isochronism which characterises the way the frequency of a mode depends on its energy e we generalize these results and show how the bifurcation energies of these modes are intimately connected to their degree of isochronism in particular we prove that in a lattice of coupled purely isochronous oscillators oscillators with an energy independent frequency the in phase mode q 0 never undergoes a tangent bifurcation whereas the out of phase mode q does provided the strength of the nonlinearity in the coupling is sufficient we derive a discrete nonlinear schrodinger equation governing the slow modulations of small amplitude band edge modes and show that its nonlinear exponent is proportional to the degree of isochronism of the corresponding orbits this equation may be seen as a link between the tangent bifurcation of band edge modes and the possible emergence of localized modes such as discrete breathers

abelian hessian algebra and commutative frobenius algebra in this paper we study the structure of an abelian hessian algebra first we show that it can be decomposed into unital abelian hessian algebras and a complete abelian hessian algebra abbreviated by caha then we show that a unital one is in fact a hyperbolic extension of a caha next we investigate the structure of caha by studying double filtration obtained canonically from lower and upper annihilator series this double filtration together with j invariant of ternary cubic form give a complete classification of caha up to dimension 6

on hack s law hack s law is reviewed emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics the relation between hack s law and the internal structure of river basins is investigated experimentally through digital elevation models it is found that hack s exponent elongation and some relevant fractal characters are closely related the self affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to hack s law an explanation for hack s law is derived from scaling arguments from the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of hack s law

quadratic conformal superalgebras abstract in this paper we shall classify quadratic conformal superalgebras by certain compatible pairs of a lie superalgebra and a novikov superalgebra four general constructions of such pairs are given moreover we shall classify such pairs related to simple novikov algebras

what controls the width function shape and can it be used for channel network comparison and regionalization 1 the width function captures the essential features of the catchment s giuh s response this paper aims to identify the morphometric properties which control the shape of the width function and assess whether these properties can be used as similarity indices for catchment comparison a new deterministic iterative model of the width function is proposed on the basis of a conceptualization of the topology of the channel network and exploiting the morphometric characteristics of internal and external nodes tests are carried out on eleven french catchments and compared to the reference peano catchment results show that the morphometric properties of three main internal and external nodes such as the drained area the distance to the outlet and the position on the channel network are useful descriptors for modeling the width function and for representing the scaling properties of a channel network while the giuhs based on horton strahler ratios are strongly related to the method used to extract the channel network from the dem the new indices are independent of the method used they are sufficient descriptors to reproduce the main shape of the width function the peak the time to peak and the main properties such as non negativity non stationarity and power law decay of the spectrum they may be used to establish catchment typology to compare catchments and to classify the width function peaks for catchment regionalization

classical waves on nonlinear lattices ii qn exact analytical solutions are found for classical vibrations of nonlinear oscillators with higher powers of spring constants such as q6 and q8 the solutions are based on a new type of elliptic function that has been created to solve these problems

new results for self similar trees with applications to river networks in a little known series of papers beginning in 1966 tokunaga introduced an infinite class of tree graphs based on the strahler ordering scheme as recognized by tokunaga 1984 these trees are characterized by a self similarity property so we will refer to them as self similar trees or ssts ssts are defined in terms of a generator matrix which acts as a blueprint for constructing different trees many familiar tree constructions are absorbed as special cases however in tokunaga s work an additional assumption is imposed which restricts from ssts to a much smaller class we will refer to this subclass as tokunaga s trees this paper presents several new and unifying results for ssts in particular the conditions under which ssts have well defined horton strahler stream ratios are given as well as a general method for computing these ratios it is also shown that the diameters of ssts grow like m where m is the number of leaves in contrast to many other tree constructions here need not equal 1 2 thus ssts offer an explanation for hack s law finally it is demonstrated that large discrepancies exist between the predictions of shreve s well known model and detailed measurements for large river networks while other ssts fit the data quite well other potential applications of the sst framework include diffusion limited aggregation dla lightning bronchial passages neural networks and botanical trees

localized excitations in two dimensional hamiltonian lattices we analyze the origin and features of localized excitations in a discrete two dimensional hamiltonian lattice the lattice obeys discrete translational symmetry and the localized excitations exist because of the presence of nonlinearities we connect the presence of these excitations with the existence of local integrability of the original n degree of freedom system on the basis of this explanation we make several predictions about the existence and stability of these excitations this work is an extension of previously published results on vibrational localization in one dimensional nonlinear hamiltonian lattices phys rev e 49 1994 836 thus we confirm earlier suggestions about the generic property of hamiltonian lattices to exhibit localized excitations independent on the dimensionality of the lattice

unit hydrograph approximations assuming linear flow through topologically random channel networks the instantaneous unit hydrograph iuh of a drainage basin is derived in terms of fundamental basin characteristics z where parameterizes the link channel segment length distribution and is a vector of hydraulic parameters z is one of three basin topological properties n n d or n m where n is magnitude number of first order streams d is diameter mainstream length and m is order the iuh is derived based on assumptions that the links are independent and identically distributed random variables and that the network is a member of a topologically random population linear routing schemes including translation diffusion and general linear routing are used and constant drainage density is assumed by using n as the fundamental basin characteristics asymptotic for large n considerations lead to a weibull probability density function for the iuh with time to peak given by tp 2n where is mean link length and is a scalar hydraulic parameter usually average celerity this asymptotic iuh is identical for all linear routing schemes

stability analysis of dynamical regimes in nonlinear systems with discrete symmetries we present a theorem that allows one to simplify the linear stability analysis of periodic and quasiperiodic nonlinear regimes in n particle mechanical systems with different kinds of discrete symmetry this theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than the dimension of the full system as an example of such a simplification we discuss the stability of bushes of modes invariant manifolds for the fermi pasta ulam chains and prove another theorem about the maximal dimension of the above mentioned subsystems

bilinear forms on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus fermionic novikov algebras correspond to a certain hamiltonian super operator in a super variable in this paper we show that there is a remarkable geometry on fermionic novikov algebras with non degenerate invariant symmetric bilinear forms which we call pseudo riemannian fermionic novikov algebras they are related to pseudo riemannian lie algebras furthermore we obtain a procedure to classify pseudo riemannian fermionic novikov algebras as an application we give the classification in dimension 4 motivated by the one in dimension 4 we construct some examples in high dimensions

conditions on the existence of localized excitations in nonlinear discrete systems we use recent results that localized excitations in nonlinear hamiltonian lattices can be viewed and described as multiple frequency excitations their dynamics in phase space takes place on tori of corresponding dimension for a one dimensional hamiltonian lattice with nearest neighbour interaction we transform the problem of solving the coupled differential equations of motion into a certain mapping m l 1 f m l m l 1 where m l for every l lattice site is a function defined on an infinite discrete space of the same dimension as the torus we consider this mapping in the tails of the localized excitation i e for l rightarrow pm infty for a generic hamiltonian lattice the thus linearized mapping is analyzed we find conditions of existence of periodic one frequency localized excitations as well as of multiple frequency excitations the symmetries of the solutions are obtained as a result we find that the existence of localized excitations can be a generic property of nonlinear hamiltonian lattices in contrast to nonlinear hamiltonian fields

commutative post lie algebra structures on nilpotent lie algebras and poisson algebras abstract we give an explicit description of commutative post lie algebra structures on some classes of nilpotent lie algebras for non metabelian filiform nilpotent lie algebras and lie algebras of strictly upper triangular matrices we show that all cpa structures are associative and induce an associated poisson admissible algebra

commutative post lie algebra structures on lie algebras abstract we show that any cpa structure commutative post lie algebra structure on a perfect lie algebra is trivial furthermore we give a general decomposition of inner cpa structures and classify all cpa structures on complete lie algebras as a special case we obtain the cpa structures of parabolic subalgebras of semisimple lie algebras

pseudo riemannian novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus pseudo riemannian novikov algebras denote novikov algebras with nondegenerate invariant symmetric bilinear forms in this paper we find that there is a remarkable geometry on pseudo riemannian novikov algebras and give a special class of pseudo riemannian novikov algebras

novikov algebras with associative bilinear forms novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus the goal of this paper is to study novikov algebras with non degenerate associative symmetric bilinear forms which we call quadratic novikov algebras based on the classification of solvable quadratic lie algebras of dimension not greater than 4 and novikov algebras in dimension 3 we show that quadratic novikov algebras up to dimension 4 are commutative furthermore we obtain the classification of transitive quadratic novikov algebras in dimension 4 but we find that not every quadratic novikov algebra is commutative and give a non commutative quadratic novikov algebra in dimension 6

from rota baxter algebras to pre lie algebras rota baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics rota baxter algebras provide a construction of pre lie algebras from associative algebras in this paper we give all rota baxter operators of weight 1 on complex associative algebras in dimension 3 and their corresponding pre lie algebras

obtaining breathers in nonlinear hamiltonian lattices we present a numerical method for obtaining high accuracy numerical solutions of spatially localized time periodic excitations on a nonlinear hamiltonian lattice we compare these results with analytical considerations of the spatial decay we show that nonlinear contributions have to be considered and we obtain very good agreement between the latter and numerical results we discuss further applications of the method and results

left symmetric algebras for mathfrak gl n we study the classification problem for left symmetric algebras with commutation lie algebra gr n in characteristic 0 the problem is equivalent to the classification of etale affine representations of g n algebraic invariant theory is used to characterize those modules for the algebraic group sl n which belong to affine etale representations of gr n from the classification of these modules we obtain the solution of the classification problem for gl n as another application of our approach we exhibit left symmetric algebra structures on certain reductive lie algebras with a one dimensional center and a non simple semisimple ideal

allometric relationships between traveltime channel networks convex hulls and convexity measures 1 the channel network s is a nonconvex set while its basin c s is convex we remove open end points of the channel connectivity network iteratively to generate a traveltime sequence of networks sn the convex hulls of these traveltime networks provide an interesting topological quantity which has not been noted thus far we compute lengths of shrinking traveltime networks l sn and areas of corresponding convex hulls c sn the ratios of which provide convexity measures cm sn of traveltime networks a statistically significant scaling relationship is found for a model network in the form l sn a c sn 0 57 from the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures new power law relations are derived such relations for a model network are cm sn and cm sn in addition to the model study these relations for networks derived from seven subbasins of cameron highlands region of peninsular malaysia are provided further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks

a zassenhaus conjecture and cpa structures on simple modular lie algebras abstract commutative post lie algebra structures on lie algebras in short cpa structures have been studied over fields of characteristic zero in particular for real and complex numbers motivated by geometry a perfect lie algebra in characteristic zero only admits the trivial cpa structure in this article we study these structures over fields of characteristic p 0 we show that every perfect modular lie algebra in characteristic p 2 having a solvable outer derivation algebra admits only the trivial cpa structure this involves a conjecture by hans zassenhaus saying that the outer derivation algebra out g of a simple modular lie algebra g is solvable we try to summarize the known results on the zassenhaus conjecture and prove some new results using the classification of simple modular lie algebras by premet and strade for algebraically closed fields of characteristic p 3 as a corollary we obtain that every central simple modular lie algebra of characteristic p 3 admits only the trivial cpa structure

hom novikov algebras we study a twisted generalization of novikov algebras called hom novikov algebras in which the two defining identities are twisted by a linear map it is shown that hom novikov algebras can be obtained from novikov algebras by twisting along any algebra endomorphism all algebra endomorphisms on complex novikov algebras of dimensions 2 or 3 are computed and their associated hom novikov algebras are described explicitly another class of hom novikov algebras is constructed from hom commutative algebras together with a derivation generalizing a construction due to dorfman and gel fand two other classes of hom novikov algebras are constructed from hom lie algebras together with a suitable linear endomorphism generalizing a construction due to bai and meng

frequency analysis of discrete breather modes using a continuous wavelet transform abstract previous theoretical and numerical studies have shown the conditions for existence and stability properties of intrinsic localized modes often refered to as discrete breathers which exist in the gaps outside the linear dispersion bands in anharmonic lattices we apply a continuous wavelet tranform to numerical simulations in order to verify some of the predicted frequency behaviour

the auslander conjecture for nil affine crystallographic groups let n be a simply connected connected real nilpotent lie group of finite dimension n we study subgroups in aff n n aut n acting properly discontinuously and cocompactly on n this situation is a natural generalization of the so called affine crystallographic groups we prove that for all dimensions 1 n 5 the generalized auslander conjecture holds i e that such subgroups are virtually polycyclic

polynomial alternatives for the group of affine motions it is known that every polycyclic by finite group even if it admits no affine structure allows a polynomial structure of bounded degree a major obstacle to a further development of the theory of these polynomial structures is that the group of the polynomial diffeomorphisms of mathbb r n in contrast to the group of affine motions is no longer a finite dimensional lie group in this paper we construct a family of finite dimensional lie groups even linear algebraic groups of polynomial diffeomorphisms which we call weighted groups of polynomial diffeomorphisms it turns out that every polycyclic by finite group admits a polynomial structure via these weighted groups in the nilpotent and other case s we can sharpen by specifying a nice set of weights the existence results obtained in earlier work we introduce unipotent polynomial structures of nilpotent groups and show how the existence of such polynomial structures is closely related to the existence of simply transitive actions of the corresponding mal cev completion this and other properties provide a strong analogy with the situation of affine structures and simply transitive affine actions considered e g in the work of fried goldman and hirsch

the automorphisms of novikov algebras in low dimensions novikov algebras were introduced in connection with poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus they also correspond to a class of vertex algebras an automorphism of a novikov algebra is a linear isomorphism satisfying xy x y which keeps the algebraic structure the set of automorphisms of a novikov algebra is a lie group whose lie algebra is just the novikov algebra s derivation algebra the theory of automorphisms plays an important role in the study of novikov algebras in this paper we study the automorphisms of novikov algebras we get some results on their properties and classification in low dimensions these results are fundamental in a certain sense and they will serve as a guide for further development moreover we apply these results to classify gel fand dorfman bialgebras and novikov poisson algebras these results also can be used to study certain phase spaces and geometric classical r matrices