low dimensional real lie algebras all real lie algebras of dimension up to 8 that admit a nontrivial levi decomposition are found

escape rates in hamiltonian systems particles escape from the vicinity of invariant tori is macroscopically modeled by a nonuniform diffusive process the space dependence of transport coefficients is fixed by using perturbation theory scalings this leads to universal predictions for the escape rates that are then observed in numerical simulations

symmetry reduction for nonlinear relativistically invariant equations symmetry reduction is studied for the relativistically invariant scalar partial differential equation h u u 2 u 0 in n 1 dimensional minkowski space m n 1 the introduction of k symmetry variables 1 k as invariants of a subgroup g of the poincare group p n 1 having generic orbits of codimension k n in m n 1 reduces the equation to a pde in k variables all codimension 1 symmetry variables in m n 1 n arbitrary reducing the equation studied to an ode are found as well as all codimension 2 and 3 variables for the low dimensional cases n 2 3 the type of equation studied includes many cases of physical interest in particular nonlinear klein gordon equations such as the sine gordon equation and hamilton jacobi equations

solvable lie algebras of dimension six six dimensional solvable lie algebras over the field of real numbers that possess nilradicals of dimension four are classified into equivalence classes this completes mubarakzyanov s classification of the real six dimensional solvable lie algebras

geometric construction of the r map from affine special real to special kahler manifolds we give an intrinsic definition of affine very special real manifolds and realise any such manifold m as a domain in affine space equipped with a metric which is the hessian of a cubic polynomial we prove that the tangent bundle n tm carries a canonical structure of affine special kahler manifold this gives an intrinsic description of the r map as the map m mapsto n tm on the physics side this map corresponds to the dimensional reduction of rigid vector multiplets from 5 to 4 space time dimensions we generalise this construction to the case when m is any hessian manifold

the poincare algebra in rank 3 simple lie algebras we classify embeddings of the poincare algebra p 3 1 into the rank 3 simple lie algebras up to inner automorphism we show that there are exactly two embeddings of p 3 1 into sl 4 c which are however related by an outer automorphism of sl 4 c next we show that there is a unique embedding of p 3 1 into so 7 c up to inner automorphism but no embeddings of p 3 1 into sp 6 c all embeddings are explicitly described as an application we show that each irreducible highest weight module of sl 4 c not necessarily finite dimensional remains indecomposable when restricted to p 3 1 with respect to any embedding of p 3 1 into sl 4 c

regular subalgebras and nilpotent orbits of real graded lie algebras abstract for a semisimple lie algebra over the complex numbers dynkin 1952 developed an algorithm to classify the regular semisimple subalgebras up to conjugacy by the inner automorphism group for a graded semisimple lie algebra over the complex numbers vinberg 1979 showed that a classification of a certain type of regular subalgebras called carrier algebras yields a classification of the nilpotent orbits in a homogeneous component of that lie algebra here we consider these problems for graded semisimple lie algebras over the real numbers first we describe an algorithm to classify the regular semisimple subalgebras of a real semisimple lie algebra this also yields an algorithm for listing up to conjugacy the carrier algebras in a real graded semisimple real algebra we then discuss what needs to be done to obtain a classification of the nilpotent orbits from that such classifications have applications in differential geometry and theoretical physics our algorithms are implemented in the language of the computer algebra system gap using our package corelg we report on example computations

constructing semisimple subalgebras of semisimple lie algebras abstract algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple lie algebra up to linear equivalence the algorithms have been used to obtain classifications of the semisimple subalgebras of the simple lie algebras of ranks 8 these have been made available as a database inside the sla package of gap 4 the subalgebras in this database are explicitly given as well as the inclusion relations among them

magic squares and matrix models of lie algebras this paper is concerned with the description of exceptional simple lie algebras as octonionic analogues of the classical matrix lie algebras we review the tits freudenthal construction of the magic square which includes the exceptional lie algebras as the octonionic case of a construction in terms of a jordan algebra of hermitian 3 3 matrices tits or various plane and other geometries freudenthal we present alternative constructions of the magic square which explain its symmetry and show explicitly how the use of split composition algebras leads to analogues of the matrix lie algebras su 3 sl 3 and sp 6 we adapt the magic square construction to include analogues of su 2 sl 2 and sp 4 for all real division algebras

definition of new equivalent indices of horton strahler ratios for the derivation of the geomorphological instantaneous unit hydrograph 1 the horton strahler concept has been important in river basin geomorphology it describes scaling properties and identifies giuh but has also attracted criticisms because it depends on the threshold area s which is used to extract the channel network from digital elevation models dem on the position of the outlet and on the few number of ratios used to identify the scaling laws to overcome these limitations this paper proposes new indices independently of s and which have similar properties than the horton strahler ratios applications were conducted on seven french basins the methodology consists on analyzing the morphometric properties such as the drained area the number of sources and the length of the channel network as a function of s the results show that horton strahler ratios vary considerably with s particularly while the order length l is a staircase function of s results show that the channel network is articulated around two main nodes independent of s which are descriptors of l then we compared the properties of horton strahler laws to those obtained from self similarity analysis which enables to define new indices independent of s these indices are calculated automatically from dem have similar properties as the horton strahler ratios and are used to calculate the giuh independently of s the four new descriptors rbe rle rae and le which have similar properties as rb rl ra and l respectively are equivalent to those of horton strahler s laws and can be used as indicators of hydrological similarity for catchment comparison and regionalization

algorithms for the tits alternative and related problems abstract we present an algorithm to decide whether a finitely generated linear group over an infinite field is solvable by finite thereby obtaining a computationally effective version of the tits alternative we also give algorithms to decide whether the group is nilpotent by finite abelian by finite or central by finite implementations of the algorithms are publicly available in magma

4 dimensional black holes from kaluza klein theories in this paper we consider generalizations in 4 dimensions of the einstein maxwell equations which typically arise from kaluza klein theories we specify conditions such that stationary solutions lead to non linear models for symmetric spaces using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in einstein maxwell theory to this more general setting

quasi conformal actions quaternionic discrete series and twistors su 2 1 and g 2 2 quasi conformal actions were introduced in the physics literature as a generalization of the familiar fractional linear action on the upper half plane to hermitian symmetric tube domains based on arbitrary jordan algebras and further to arbitrary freudenthal triple systems in the mathematics literature quaternionic discrete series unitary representations of real reductive groups in their quaternionic real form were constructed as degree 1 cohomology on the twistor spaces of symmetric quaternionic kahler spaces these two constructions are essentially identical as we show explicitly for the two rank 2 cases su 2 1 and g2 2 we obtain explicit results for certain principal series quaternionic discrete series and minimal representations of these groups including formulas for the lowest k types in various polarizations we expect our results to have applications to topological strings black hole micro state counting and to the theory of automorphic forms

on a connection between kam and nekhoroshev s theorems abstract using the iteration of nekhoroshev s theorem as a basic tool we point out the existence of a hierarchic structure of nested domains underlying the phenomenon of diffusion at each level we find that the diffusions speed is exponentially small with respect to the previous level the set of kam tori is the domain characterized by a zero diffusion speed

the classification of the perfect cyclic sl n 1 cn 1 modules abstract a perfect cyclic module of a perfect lie algebra g with solvable radical r and levi decomposition g s r is a finite dimensional module of g generated by an irreducible module of the semisimple lie algebra s in this paper we classify all the perfect cyclic finite dimensional indecomposable modules of the perfect lie algebras sl n 1 c n 1 given by the semidirect sum of the simple lie algebra a n with its standard representation furthermore using the embedding of the lie algebra sl n 1 c n 1 in sl n 2 we show that any finite dimensional irreducible module of sl n 2 restricted to sl n 1 c n 1 is a perfect cyclic module and that any perfect cyclic sl n 1 c n 1 module can be constructed as quotient module of the restriction to sl n 1 c n 1 of some finite dimensional irreducible sl n 2 module this explicit realization of the perfect cyclic sl n 1 c n 1 modules plays a role in their classification

on self similarity and self affinity of drainage basins an approach is proposed which allows consideration from common positions the self similar and self affine properties of river drainage basins and which introduces respective characteristics of their fractal structure horton s 1945 model has been assumed as the basis of this study it is shown that self similarity of river drainage basins is characterized by the self similarity dimension ds ln rb ln rl in the case of self affinity two scaling indices dl ln rb ln rl and dw ln rb ln ra rl are required the combinations of which determine the hurst h dl dw index characterizing the degree of drainage basins self affinity and the lacunary dimension dg 2dldw dl dw characterizing the degree of lacunarity or noncompactness of drainage basins on the basis of analysis of published data from rivers in the united states italy russia and romania the conclusion is drawn that river drainage basins are generally noncompact dg 2 and self affine h 1 fractal objects besides for a quantitative description of river drainage basins a new parameter is introduced which characterizes the degree to which a large catchment is filled with smaller ones

levi decomposable subalgebras of the symplectic algebra c2 the semisimple subalgebras of the symplectic algebra c2 are well known in this article we classify the levi decomposable subalgebras of the symplectic algebra c2 up to inner automorphism by levi s theorem a full classification of the subalgebras of c2 would be complete with a classification of its solvable subalgebras

fractal relation of mainstream length to catchment area in river networks institute of hydraulics university of genoa italymandelbrot s 1982 hypothesis that river length is fractal has been recently substantiated byhjelmfelt 1988 using eight rivers in missouri the fractal dimension of river length d is derived herefrom the horton s laws of network composition this results in a simple function of stream length andstream area ratios that is d max 1 2 log rl og ra three case studies are reported showing thisestimate to be coherent with measurements of d obtained from map analysis the scaling properties ofthe network as a whole are also investigated showing the fractal dimension of river network d todepend upon bifurcation and stream area ratios according to d min 2 2 log rb log ra theseresults provide a linkage between quantitative analysis of drainage network composition and scalingproperties of river networks

fixed mass multifractal analysis of river networks and braided channels a fixed mass multifractal fma analysis was used to investigate natural river networks and braided channels in particular while the study of natural river networks was performed with fixed size algorithms fsas in the past the analysis of natural braided channels was not pursued before to our knowledge results showed the multifractal and non plane filling nature of all the digitalized data sets analysis of the digitalization step constant or not was performed and showed that it does not exert a strong influence on the assessed values of the lipschitz holder exponents and the support dimensions even if a constant step permits better reconstruction of the right sides of the spectra for negative moment orders of probabilities the fma approach presented two improvements with respect to the fsa one in terms of oscillations of the scaling curves for negative moment orders of probabilities and of error bars a more precise assessment of the multifractal spectra is of great importance in the development of multifractal models for the simulation of flood hydrographs

embeddings of the euclidean algebra e 3 into sl 4 c and restrictions of irreducible representations of sl 4 c the euclidean group e 3 is the lie group of orientation preserving isometries of three dimensional euclidean space it is the noncompact semidirect product group e 3 so 3 r3 the euclidean algebra e 3 is the complexification of the lie algebra of e 3 we classify the embeddings of the euclidean algebra e 3 into the simple lie algebra sl 4 c and as an application of this classification discuss the restriction to various embeddings of e 3 of certain irreducible representations of sl 4 c in particular we consider which of these restrictions are e 3 indecomposable

maximal abelian subalgebras of pseudounitary lie algebras abstract the task of classifying and constructing all maximal abelian subalgebras of su p q p q 1 is reduced to that of classifying orthogonally indecomposable masas these are either maximal abelian nilpotent subalgebras represented by nilpotent matrices in any finite dimensional representation or for p q they can be nonorthogonally decomposable and their study can be reduced to a construction of manss of sl p c two types of manss of su p q are shown to exist one rowed and non one rowed numerous classification theorems are proven and applied to obtain all masas of su p 1 su p 2 and su p q with p q 6 physical applications are discussed

directed recursion models for fractal growth fractals constructed by recursive processes are introduced to model growth phenomena these fractals are simultaneously directed and self similar in analogy with patterns growing under diffusion limited conditions the multifractal nature of the harmonic measure associated with laplacian interfaces is qualitatively interpreted using the models calculation of the largest singularity exponent allows one to make conclusions about the behaviour of diffusion limited aggregates

the schrodinger langevin equation special solutions and nonexistence of solitary waves two types of solutions of the schrodinger langevin equation are investigated it is proved that a special type of gaussian solutions exist globally in time for the harmonic oscillator hamiltonian furthermore it is shown that the schrodinger langevin equation can have no solitary wave type solutions in the damped free particle case which lie in l2

symmetry reduction for the kadomtsev petviashvili equation using a loop algebra the kadomtsev petviashvili kp equation ut 3uux 2 1 4 uxxx x 3 uyy 4 0 allows an infinite dimensional lie group of symmetries i e a group transforming solutions amongst each other the lie algebra of this symmetry group depends on three arbitrary functions of time t and is shown to be related to a subalgebra of the loop algebra a 1 4 low dimensional subalgebras of the symmetry algebra are identified specifically all those of dimension n 3 and also a physically important six dimensional lie algebra containing translations dilations galilei transformations and quasirotations new solutions of the kp equation are obtained by symmetry reduction using the one dimensional subalgebras of the symmetry algebra these solutions contain up to three arbitrary functions of t

conformal and quasiconformal realizations of exceptional lie groups we present a nonlinear realization of e8 8 on a space of 57 dimensions which is quasiconformal in the sense that it leaves invariant a suitably defined light cone in 57 this realization which is related to the freudenthal triple system associated with the unique exceptional jordan algebra over the split octonions contains previous conformal realizations of the lower rank exceptional lie groups on generalized space times and in particular a conformal realization of e7 7 on 27 which we exhibit explicitly possible applications of our results to supergravity and m theory are briefly mentioned

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

on nilpotent generators of the lie algebra sln abstract consider the special linear lie algebra sl n k over an infinite field of characteristic different from 2 we prove that for any nonzero nilpotent x there exists a nilpotent y such that the matrices x and y generate the lie algebra sl n k

superexponential stability of kam tori we study the dynamics in the neighborhood of an invariant torus of a nearly integrable system we provide an upper bound to the diffusion speed which turns out to be of superexponentially small size exp exp 1 being the distance from the invariant torus we also discuss the connection of this result with the existence of many invariant tori close to the considered one

high order control for symplectic maps abstract we revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium using a technique based on lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow the formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation then we perform an heuristic analysis of the dynamical behavior of the map using the invariant function for the normalized map finally we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map the numerical examples are worked out on a two dimensional map of henon type

multifractal analysis of river networks sandbox approach 1 two fixed size algorithms were used to investigate natural river networks the box counting method and the sandbox method the first produces good results for nonnegative moment orders q but suffers from border effects the second solves border problems and is particularly adapted to negative moment orders for the reconstruction of the right side of the multifractal spectrum f in the box counting applications the influence of the mesh number was investigated in the range 20 to 100 for moment orders from 0 to 10 showing that the error in the assessment of the generalized fractal dimensions is not greater than 3 the sandbox method was applied to the river networks for the first time and the theoretical expression of the information entropy was derived results were obtained also for negative moment orders showing that the analyzed river networks are multifractal and non plane filling structures the sandbox method avoids border effects as verified through an application to a square portion extracted from a river network result analysis suggests a dependence of the f spectra from the lithologic characteristics of the source rocks

2 generation of simple lie algebras and free dense subgroups of algebraic groups abstract we construct generating pairs of simple lie algebras in characteristic zero we apply this construction to exhibit infinite series of 2 generator zariski dense subgroups that are free of rank 2 of the simple algebraic groups sl n c sp n c g 2 c

scale invariance properties of the peak of the width function in topologically random networks some scaling properties of the topological width function for an infinite population of networks obeying the random model are analyzed a monte carlo procedure is applied to generate width functions according to the hypothesis of topological randomness the probability distributions of both peak and distance to peak of the topological width functions conditioned 1 on the network diameter and 2 on and parameter log 2 l log are studied the parameter can be considered a shape factor of the network indeed low values describe elongated networks while high values refer to fan like networks scale invariance for both random variables is established in the first case by using as a scale parameter also in the second case scale invariance is observed for both the peak and the distance to peak of the topological width function in particular the invariance property for the peak involves a scaling function which is directly related to the shape factor allowing determination of the statistical similarity between random networks indexed by the same then a coarse graining procedure is applied to a set of 15 000 width functions with 512 a scaling behavior of peaks of the original width function and aggregated ones is observed over a wide range of aggregation scales consequently a statistical self similarity for the peaks is also observed which involved the same related scaling function finally possible implication of the present results on the hydrologic response at the basin scale is discussed

the subalgebras of the rank two symplectic lie algebra abstract the semisimple subalgebras of the rank 2 symplectic lie algebra sp 4 c are well known and we recently classified its levi decomposable subalgebras in this article we classify the solvable subalgebras of sp 4 c up to inner automorphism this completes the classification of the subalgebras of sp 4 c more broadly speaking in completing the classification of the subalgebras of sp 4 c we have completed the classification of the subalgebras of the rank 2 semisimple lie algebras

the euclidean algebra in rank 2 classical lie algebras we classify the embeddings of the euclidean algebra e 2 into the rank 2 semisimple classical lie algebras the classifications are up to inner automorphism we also examine the finite dimensional irreducible representations of the rank 2 semisimple classical lie algebras restricted to e 2 with respect to various embeddings all lie algebras and representations are over the complex numbers

closed subsets of root systems and regular subalgebras abstract we describe an algorithm for classifying the closed subsets of a root system up to conjugation by the associated weyl group our algorithm is implemented in the language of the computer algebra system gap 4 we discuss the implementation and give runtimes on some sample inputs the classification of the closed subsets of an irreducible root system is closely related to the classification of the regular subalgebras up to inner automorphism of the corresponding simple lie algebra we show how to obtain the regular subalgebras corresponding to a given closed set for the root systems of rank 3 the version of this paper on the arxiv has tables describing the subalgebras that were obtained

fractal structure and properties of stream networks this paper studies the fractal structure and properties of stream networks through a comparison between stream networks and loopless random aggregate trees five fractal dimensions are recognized for stream networks namely topological dimension dt minimum path dimension dm fractal dimension of stream networks as a whole df diffusion dimension dw and spectral dimension ds mathematical definitions and derivations of the fractal dimensions are proposed which provide a theoretical basis for some recognized empirical relationships in drainage basin geomorphology relationships among the fractal dimensions are examined and the average values of the fractal dimensions for natural stream networks are estimated the hydrological implications of the fractal dimensions of stream networks are also discussed

reexamining the determination of the fractal dimension of river networks in analyzing the literature on the fractal nature of river networks one can recognize several points that require clarification or additional investigations for instance many interpretations with different conclusions have been given to the important empirical results found in the previous literature on river geomorphology similarly the argument concerning a possible more likely value of the fractal dimensions of river networks has not yet found a convincing answer in an attempt to shed more light on the topic particularly on the latter point we have reexamined the basic aspects related to selfsimilarity in river networks using uniquely the fundamental concepts of fractal geometry this approach leads to relations for the determination of the fractal dimensions which hold exactly for deterministic self similar trees and are compatible with related findings reported in literature results obtained from application of these relations to several river networks in southern italy indicate very low variability around the average values of about 1 7 1 5 and 1 1 for the fractal dimensions of the whole river network of its topological equivalent and of its individual streams respectively this outcome in addition to comparable results taken from the literature provides new arguments to the hypothesis that natural networks tend to have the same fractal dimensions

detection of arnold diffusion in hamiltonian systems we detect diffusion along resonances in a quasi integrable system at small values of the perturbing parameter the diffusion coefficient goes to zero as the perturbation parameter goes to zero faster than a power law typical of chirikov diffusion and is compatible with an exponential law expected in the nekhoroshev theorem

measuring the mixing efficiency in a simple model of stirring some analytical results and a quantitative study via frequency map analysis we prove the existence of invariant curves for a t periodic hamiltonian system which models a fluid stirring in a cylindrical tank when t is small and the assigned stirring protocol is piecewise constant furthermore using the numerical analysis of the fundamental frequency of laskar we investigate numerically the break down of invariant curves as t increases and we give a quantitative estimate of the efficiency of the mixing

fractal geometry of individual river channels and its computer simulation a new method for analyzing the self similarity and self affinity of single thread channels is proposed it permits the determination of the fractal scaling exponents of the characteristic scales and the evaluation of the degree of anisotropy for self similar fractal lines based upon the application of this method to the dniester and pruth rivers we established the self similarity of the river pattern on small scales and the self affinity on large scales for these rivers we obtained the fractal scaling exponents the characteristic scales and the anisotropy parameters a computer model has been developed which simulates river patterns whose fractal properties are close to the properties of natural objects a generalized model of fractal behavior of natural rivers is proposed on the basis of self affinity of natural and simulated rivers on large scales a hypothesis has been formulated which explains the violation of the dimension principle in the well known relation between the river length and the catchment area

on dense free subgroups of lie groups abstract we give a method for constructing dense and free subgroups in real lie groups in particular we show that any dense subgroup of a connected semisimple real lie group g contains a free group on two generators which is still dense in g and that any finitely generated dense subgroup in a connected non solvable lie group h contains a dense free subgroup of rank 2 dim h this answers a question of carriere and ghys and it gives an elementary proof to a conjecture of connes and sullivan on amenable actions which was first proved by zimmer

horton s laws and the fractal nature of streams stream networks and catchment basins are characterized by numerous fractal dimensions the traditional one being the mainstream length as a function of length scale which we denote by d we consider an ideal horton system and define fractal dimensions based on 1 the subcatchment length area relationship which gives d1 2 the total length of streams as a function of scale which gives a network similarity dimension d2 3 the mainstream length area relationship d3 and 4 the total area of streams as a function of areal scale d4 these fractal dimensions are related to the values of the bifurcation ratio the stream length ratio and the stream area ratio their value should be indirectly estimated from these horton parameters an improved understanding of the relationships between the fractal dimension and horton s laws is obtained by defining an eigenarea of a stream of a particular horton order this is the area of the drainage basin which is not drained by streams of immediately lower order the variation of eigenareas with scale controls the value of d1 which equals d3 for hydrologically realistic systems in such cases d4 2 this paper assumes that river systems are hortonian in nature and that measured departures from hortonianity are due to statistical variability estimates of the horton parameters and of the fractal dimensions are therefore subject to uncertainty two sources of statistical variability are considered herein the first source of statistical variability is due to the fluctuations in stream numbers stream lengths and stream areas these fluctuations affect the values of the horton parameters which are traditionally estimated using a graphical technique we show that an analytical technique which corresponds to a constrained graphical technique is preferable the second source of variability that we consider arises from the fact that estimates of horton s parameters and fractal dimensions are always made on truncated systems because the particular scales of measurement determine the order of the catchment in a horton system it is straight forward to estimate d1 which is defined exactly at all scales direct attempts to estimate d2 and d3 as opposed to indirect attempts via the horton parameters are difficult because their true value is approached asymptotically in the limit of infinite order catchments

a note on fractal channel networks this paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response a mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry in view of the connectivity conjecture horton s bifurcation ratio r b tends for high values of strahler s order omega of the basin to the area ratio r a and horton s length ratio r l equals in the limit the single order contributing area ratio r a the relevance of these arguments is examined by reference to data from real basins well known empirical results from the geomorphological literature melton s law hack s relation moon s conjecture are viewed as a consequence of connectivity it is found that in hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1 r b the application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph in particular generalizing its width function formulation a quantitative example of multifractal hydrologic response of idealized networks based on peano s construct for which r b r a 4 r l 2 closes the paper

levi decomposable algebras in the classical lie algebras abstract we examine embeddings of an important class of levi decomposable algebras into the classical lie algebras in particular we classify the embeddings of a n c n 1 b n c 2 n 1 c n c 2 n and d n c 2 n into the complex simple lie algebras a n 1 b n 1 c n 1 and d n 1 respectively up to inner automorphism

river network fractal geometry and its computer simulation the hierarchical ordinal and statistical models of river networks are proposed their investigation has been carried out on the basis of river networks computer simulation as well as on empirical data analysis the simulated river networks display self similar behavior on small scales the fractal dimension d 1 52 and hurst s exponent h 1 0 and self affine behavior on large scales the lacunary dimension dg 1 71 h 0 58 similar behavior is also qualitatively characteristic for natural river networks for catchment areas from 142 to 63 700 km2 we obtained dg 1 87 and h 0 73 thus in both cases one finds a region of scales with self affine behavior h 1 and with dg 2 proceeding from fractal properties of the river networks the theoretical basis of scaling relationships l a and ae widely used in hydrology are given l and a denote the main river length the total length of the river network and catchment area respectively 1 1 h and e dg 2

on symmetric attractors in reversible dynamical systems abstract let o n be a finite group acting orthogonally on r n we say that is a reversing symmetry group of a homeomorphism diffeomorphism or flow f t r n r n t z or t r if has an index two subgroup whose elements commute with ft and for all elements and all t ft x f t x we give necessary group and representation theoretic conditions for subgroups of reversing symmetry groups to occur as symmetry groups of attractors lyapunov stable limit sets these conditions arise due to topological obstructions in dimensions 1 and 2 we present a complete description of possible symmetry groups of asymptotically stable attractors for homeomorphisms and diffeomorphisms these attractors cannot possess reversing symmetries we also have a fairly complete description in the context of subgroups which contain reversing symmetries for all dimensions n we present complete results on the possible symmetry groups of connected asymptotically stable attractors in addition we summarize our results in the context of reversible equivariant flows which are complete in dimensions 1 and 2 as well as for subgroups of o n in any dimension n a survey of the corresponding results in the equivariant context is also given