systems of numeration and fractal functions relating to substitutions french abstract let a be a finite alphabet a substitution over a un n n a fixed point for and for each a a a a real number we establish under some assumptions an asymptotic formula concerning the sum s n i n u i n n this result generalizes some previous results from coquet or brillhart erdos and morton moreover relations with self affine functions in a sense which generalizes a definition from kamae are proved the calculi leave over systems of representation of integers and real numbers

symmetrized β integers this article deals with b numeration systems which are numeration systems with a non integral base b 1 in this framework there exist elements which naturally play the role of integers which are called b integers the set of non negative b integers denoted by z b has various equivalent definitions which arise from different points of view nevertheless these definitions may be generalized on negative real numbers in a non unique way depending on the chosen framework we focus in this article on confluent parry units they are the positive roots of the polynomials x d i 1 d 1kx i 1 where the integers d and k satisfy d 2 and k 1 for any of these numbers we prove that there exists a discrete subset of r that we denote by z b s which is locally isomorphic to z b and such that z b s z b s moreover z b s is a model set and satisfies the inflation property there exists l 1 such that lz b s z b s l is then called the inflation factor for z b s finally we compute inflation factors for z b s of the form b i i being a positive integer

the asymptotic distribution of elements in automatic sequences in an automatic sequence an element need not have an asymptotic density in this paper a necessary and sufficient criterion is proved for the existence of the asymptotic density of a given element if it does not exist the asymptotic distribution of the element can be described in terms of a function h whose graph is self similar an algorithm is given to decide whether h is piecewise continuously differentiable and in this case it can be computed effectively finally it is shown that the h density of an element in an automatic sequence always exists and equals its logarithmic density

asymptotic expansions for linear homogeneous divide and conquer recurrences algebraic and analytic approaches collated among all sequences that satisfy a divide and conquer recurrence those which are rational with respect to a numeration system are certainly the most basic and the most essential nevertheless until recently this specific class of sequences has not been systematically studied from the asymptotic standpoint we recall how a mechanical process designed by the author permits to compute their asymptotic expansions the process is based on linear algebra and involves computing jordan normal forms joint spectral radii and solving dilation equations the main contribution of the present article is the comparison between our algebraic method and the classical analytic number theory approach moreover we develop new ways to compute the fourier series of the periodic functions involved in the expansion the article comes with an extended bibliography

a markov partition that reflects the geometry of a hyperbolic toral automorphism we show how to construct a markov partition that reflects the geometrical action of a hyperbolic automorphism of the n torus the transition matrix is the transpose of the matrix induced by the automorphism in u dimensional homology provided this is non negative here u denotes the expanding dimension that condition is satisfied at least for some power of the original automorphism under a certain non degeneracy condition on the galois group of the characteristic polynomial the nu rectangles are constructed by an iterated function system and they resemble the product of the projection of a u dimensional face of the unit cube onto the unstable subspace and the projection of minus the orthogonal n u dimensional face onto the stable subspace

palindromic length of words and morphisms in class p abstract we study the palindromic length of factors of infinite words fixed by morphisms of the so called class p introduced by hof knill and simon we show that it grows at most logarithmically with the length of the factor for the fibonacci word and the thue morse word we provide explicit bounds on their rate of growth we also construct an infinite word rich in palindromes for which the palindromic length grows as n

substitution dynamical systems characterization of linear repetitivity and applications we consider dynamical systems arising from substitutions over a finite alphabet we prove that such a system is linearly repetitive if and only if it is minimal based on this characterization we extend various results from primitive substitutions to minimal substitutions this includes applications to random schrodinger operators and to number theory

on estimation of monotone and concave frontier functions abstract when analyzing the productivity of firms one may want to compare how the firms transform a set of inputs x typically labor energy or capital into an output y typically a quantity of goods produced the economic efficiency of a firm is then defined in terms of its ability to operate close to or on the production frontier the boundary of the production set the frontier function gives the maximal level of output attainable by a firm for a given combination of its inputs the efficiency of a firm may then be estimated via the distance between the attained production level and the optimal level given by the frontier function from a statistical viewpoint the frontier function may be viewed as the upper boundary of the support of the population of firms density in the input and output space it is often reasonable to assume that the production frontier is a concave monotone function then a famous estimator in the univariate input and output case is the data envelopment analysis dea estimato

a simple variational approach to a converse of the lagrange dirichlet theorem peter hagedorn 8r jean mawhin communicated by k kigc g ssner 1 introduction the lagrange dirichlet stability theorem states that the equilibrium posi tion of a discrete conservative mechanical sytem is stable in the sense of liapunov if the potential energy u assumes a strict local minimum at this equilibrium we know from painzev s example 22 see also 37 that this sufficient condition stated by lagranoe 13 and proved by lejevne dirich et 17 is not necessary for stability and the history of the inversion of the lagrange dirichlet theorem i e of the search for necessary conditions for stability is rich and interesting we refer to 27 for a discussion and a bibliography and to the more recent references 1 3 6 12 14 16 18 20 21 23 26 28 32 35 36 in 1971 ha6edorn proved for systems of class c 2 that the equilibrium position is unstable if the potential energy u has a strict maximum at this equilibrium 4 5 this result was extended in various directions by ta l fer o 30 bomtin kozlov 2 kozmv 10 liubushin 18 and sofer 29 a common feature of all those proofs initiated in 4 is the application of some method of the calculus of variations namely the theory of geodesics on finsler manifolds to jacobi s form of the principle of least action this leads to technical difficulties which are overcome in the above mentioned papers through a lot of effort and ingenuity the aim of this short paper is to show that the replacement of jacobi s principle of least action by a variant of another variational principle recently introduced by van groesen 33 34 in the study of normal mode vibrations of conservative nonlinear systems allows a simple and elementary treatment in the setting of a hilbert space instead of a finsler manifold of the instabili ty theorem stated in 4 with the minimal regularity assumptions of 18 29 30 in this way the problem is reduced to proving the existence of a minimum for a coercive functional defined on a weakly closed subset of a hilbert space a problem solved at the beginning of any monograph on the direct methods of the calculus of variations see e g 19 the reduction

tilings induced by a class of cubic rauzy fractals we study aperiodic and periodic tilings induced by the rauzy fractal and its subtiles associated with beta substitutions related to the polynomial x 3 ax 2 bx 1 for a b 1 in particular we compute the corresponding boundary graphs describing the adjacencies in the tilings these graphs are a valuable tool for more advanced studies of the topological properties of the rauzy fractals as an example we show that the rauzy fractals are not homeomorphic to a closed disc as soon as a 2b 4 the methods presented in this paper may be used to obtain similar results for other classes of substitutions

rational self affine tiles an integral self affine tile is the solution of a set equation mathbf a mathcal t bigcup d in mathcal d mathcal t d where mathbf a is an n times n integer matrix and mathcal d is a finite subset of mathbb z n in the recent decades these objects and the induced tilings have been studied systematically we extend this theory to matrices mathbf a in mathbb q n times n we define rational self affine tiles as compact subsets of the open subring mathbb r n times prod mathfrak p k mathfrak p of the adele ring mathbb a k where the factors of the finite product are certain mathfrak p adic completions of a number field k that is defined in terms of the characteristic polynomial of mathbf a employing methods from classical algebraic number theory fourier analysis in number fields and results on zero sets of transfer operators we establish a general tiling theorem for these tiles we also associate a second kind of tiles with a rational matrix these tiles are defined as the intersection of a translation of a rational self affine tile with mathbb r n times prod mathfrak p 0 simeq mathbb r n although these intersection tiles have a complicated structure and are no longer self affine we are able to prove a tiling theorem for these tiles as well for particular choices of digit sets intersection tiles are instances of tiles defined in terms of shift radix systems and canonical number systems therefore we gain new results for tilings associated with numeration systems

a gamma moment approach to monotonic boundary estimation the estimation of optimal support boundaries under the monotonicity constraint is relatively unexplored and still in full development this article examines a new extreme value based model which provides a valid alternative for complete envelopment frontier models that often suffer from lack of precision and for purely stochastic ones that are known to be sensitive to model misspecification we provide different motivating applications including the estimation of the minimal cost in production activity and the assessment of the reliability of nuclear reactors

algebraic numbers free group automorphisms and substitutions on the plane there has been much recent work on the geometric representation of pisot substitutions and the explicit construction of markov partitions for pisot toral automorphims we give a construction that extends this to the general hyperbolic case for the sake of simplicity we consider a simple example of an automorphism of the free group on 4 generators whose associated matrix has 4 distinct complex eigenvalues two of them of modulus larger than 1 and the other 2 of modulus smaller than 1 non pisot case using this generator we build substitution polygonal tilings of the contracting plane and the expanding plane of the matrix we prove that these substitution tilings can be lifted in a unique way to stepped surfaces approximating each of these planes the vertices of each of these stepped surfaces can be projected to an atomic surface a compact set with fractal boundary contained in the other plane we prove that both tilings can be refined to exact self similar tilings whose tiles have fractal boundaries and can be obtained by iteration or by a cut and project method by using the atomic surface as the window using the self similar tiling one can build a numeration system associated to a complex lambda expansion the natural extension of the lambda expansion associated with this number system is the linear map obtained by abelianization of the free group automorphism this gives an explicit markov partition of this hyperbolic toral automorphism the fractal domains can be used to define a pseudo group of translations which gives transversal dynamics in the sense of vershik 1994 or numeration systems in the sense of kamae 2005 the construction can be extended to a larger class of free group automorphisms each of which can be used to build substitution rules and dynamical systems

smooth words over arbitrary alphabets smooth infinite words over 1 2 are connected to the kolakoski word k 221121 defined as the fixpoint of the function that counts the length of the runs of 1 s and 2 s in this paper we extend the notion of smooth words to arbitrary alphabets and study some of their combinatorial properties using the run length encoding every word is represented by a word obtained from the iterations of in particular we provide a new representation of the infinite fibonacci word f as an eventually periodic word on the other hand the thue morse word is represented by a finite one

on the joint subword complexity of automatic sequences let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m denotes the number of distinct blocks u n u n m 1 of size m in u in this paper we study the complexity of u n u 1 n u r n n 0 when each u i u i n n 0 i 1 r is a q i automatic sequence over a finite set s i and q 1 q r 2 are pairwise coprime integers as an application we answer a question of allouche and shallit regarding morphic real numbers

abelian properties of parry words abelian complexity of a word u is a function that counts the number of pairwise non abelian equivalent factors of u of length n we prove that for any c balanced parry word u the values of the abelian complexity function can be computed by a finite state automaton the proof is based on the notion of relative parikh vectors the approach works for any function f n that can be expressed in terms of the set of relative parikh vectors corresponding to the length n for example we show that the balance function of a c balanced parry word is computable by a finite state automaton as well

asymptotic orbits of primitive substitutions a primitive aperiodic substitution on d letters has at most d2 asymptotic orbits this bound is sharp since asymptotic arc components in tiling spaces associated with substitutions are in 1 1 correspondence with asymptotic words this provides a bound for those as well

asymptotic distribution of conical hull estimators of directional edges non parametric data envelopment analysis dea estimators have been widely applied in analysis of productive efficiency typically they are de ned in terms of convex hulls of the observed combinations of inputs outputs in a sample of enterprises the shape of the convex hull relies on hypothesis on the shape of the technology de ned as the boundary of the set of technically attainable points in the inputs outputs space so far only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered which corresponds to a situation where the technology presents varying returns to scale vrs this paper analyzes the case where the most common constant returns to scale crs hypothesis is assumed here the dea is de ned as the smallest conical hull with vertex at the origin enveloping the cloud of observed points in this paper we determine the asymptotic properties of this estimator showing that the rate of convergence is better than for the vrs estimator we derive also its asymptotic sampling distribution with a practical way to simulate it this allows to de ne a bias corrected estimator and to build con dence intervals for the frontier we compare in a simulated example the bias corrected estimator with the original conical hull estimator and show its superiority in terms of median squared error

geometric theory of unimodular pisot substitutions we are concerned with the tiling flow t associated to a substitution over a finite alphabet our focus is on substitutions that are unimodular pisot i e their matrix is unimodular and has all eigenvalues strictly inside the unit circle with the exception of the perron eigenvalue 1 the motivation is provided by the still open conjecture asserting that t has pure discrete spectrum for any such we develop a number of necessary and sufficient conditions for pure discrete spectrum including injectivity of the canonical torus map the geometric realization geometric coincidence condition partial commutation of t and the dual r d 1 action measure and tiling properties of rauzy fractals and concrete algorithms some of these are original and some have already appeared in the literature as sufficient conditions only but they all emerge from a unified approach based on the new device the strand space f of the proof of the necessity hinges on determination of the discrete spectrum of t as that of the associated kronecker toral flow

ramsey theory in noncommutative semigroups by utilizing ultrafilters we give a general version of the central sets theorem 6 proposition 8 21 this enables us to derive noncommutative versions of van der waerden s theorem and several of its generalizations we also derive some standards results including the hales jewett theorem

set polynomials and polynomial extension of the hales jewett theorem an abstract hales jewett type extension of the polynomial van der waerden theorem bl is established theorem let r d q n there exists n n such that for any r coloring of the set of subsets of v 1 n d 1 q there exist a set a v and a nonempty set 1 n such that a d 1 q and the subsets a a d 1 a d 2 a d q are all of the same color this polynomial hales jewett theorem contains refinements of many combinatorial facts as special cases the proof is achieved by introducing and developing the apparatus of set polynomials polynomials whose coefficients are finite sets and applying the methods of topological dynamics

on the stable equilibrium points of gradient systems this paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f in particular it is shown that under the assumption that f is real analytic local minimality is necessary and sufficient for stability under the weaker assumption that f is indefinitely continuously differentiable local minimality is neither necessary nor sufficient for stability

dual systems of algebraic iterated function systems abstract we study a class of graph directed iterated function systems on r with algebraic parameters which we call algebraic gifs we construct a dual ifs of an algebraic gifs and study the relations between the two systems we determine when a dual system satisfies the open set condition which is fundamental for feasible pisot systems we construct the left and right rauzy thurston tilings and study their multiplicities and decompositions we also investigate their relation with codings space domain exchange transformation and the pisot spectrum conjecture the dual ifs provides a unified and simple framework for rauzy fractals tilings and related studies and allows us gain better understanding

morphic words and equidistributed sequences abstract the problem we consider is the following given an infinite word w on an ordered alphabet construct the sequence w n n equidistributed on 0 1 and such that m n if and only if m w n w where is the shift operation erasing the first symbol of w the sequence w exists and is unique for every word with well defined positive uniform frequencies of every factor or in dynamical terms for every element of a uniquely ergodic subshift in this paper we describe the construction of w for the case when the subshift of w is generated by a morphism of a special kind then we overcome some technical difficulties to extend the result to all binary morphisms the sequence w in this case is also constructed with a morphism at last we introduce a software tool which given a binary morphism computes the morphism on extended intervals and first elements of the equidistributed sequences associated with fixed points of

on chaotic minimal center of attraction of a lagrange stable motion for topological semi flows abstract let f r x x be a topological semi flow on a polish space x in 1977 karl sigmund conjectured that if there is a point x in x such that the motion f x has just x as its minimal center of attraction then all such x form a residual subset of x in this paper we first present a positive solution to this conjecture and then apply it to the study of chaotic dynamics occurring inside or near the minimal center of attraction of a motion f x

nonmetrizable topological dynamics and ramsey theory applying ideas from topological dynamics in compact metric spaces to the stone cech compactification of a discrete semigroup several new proofs of old results and some new results in ramsey theory are obtained in particular two ultrafilter proofs of van der waerden s theorem are given an ultrafilter approach to central sets sets which are combinatorially rich is developed this enables us to show that for any partition of the positive integers one cell is both additively and multiplicatively central also a fortuitous answer to a question of ellis is obtained

separators in infinite words generated by morphisms resume nous appelons separateur d un mot x a l indice n e n le plus petit facteur de x dont l indice du debut de la premiere occurrence est n notons sx n la longueur de ce separateur lorsqu il existe et posons sx n 0 sinon nous montrons que l application sx ainsi definie est q reguli e re au sens d allouche et shallit lorsque x est un mot infini engendre par iteration d un morphisme q uniforme et que x est circulaire de maniere equivalente cela revient a dire que la serie formelle dont les coefficients sont les valeurs sx n en base q est n rationnelle salomaa soittola

multiplicative richness of additively large sets in zd abstract in their proof of the ip szemeredi theorem a far reaching extension of the classic theorem of szemeredi on arithmetic progressions furstenberg and katznelson 14 introduced an important class of additively large sets called ip r sets which underlies recurrence aspects in dynamics and is instrumental to enhanced formulations of combinatorial results the authors recently showed that additive ip r subsets of z d are multiplicatively rich with respect to every multiplication on z d without zero divisors e g multiplications induced by degree d number fields in this paper we explain the relationships between classes of multiplicative largeness with respect to different multiplications on z d we show for example that in contrast to the case for z there are infinitely many different notions of multiplicative piecewise syndeticity for subsets of z d when d 2 this is accomplished by using the associated algebra representations to prove the existence of sets which are large with respect to some multiplications while small with respect to others in the process we give necessary and sufficient conditions for a linear transformation to preserve a class of multiplicatively large sets one consequence of our results is that additive ip r sets are multiplicatively rich in infinitely many genuinely different ways we conclude by cataloging a number of sources of additive ip r sets from combinatorics and dynamics

on the influence of the kinetic energy on the stability of equilibria of natural lagrangian systems natural lagrangian systems t on r2 described by the equation frac d dt frac partial t partial dot q frac partial t partial q frac partial pi partial q are considered where t q q is a positive definite quadratic form in q and q has a critical point at 0 it is constructively proved that there exist a c potential energy and two c kinetic energies t and t such that the equilibrium q t 0 is stable for the system t and unstable for the system t equivalently it is established that for c natural systems the kinetic energy can influence the stability in the analytic category this is not true

additive and multiplicative properties of point sets based on beta integers to each number 1 correspond abelian groups in rd of the form i 1d z ei which obey the set z of beta integers is a countable set of numbers it is precisely the set of real numbers which are polynomial in when they are written in basis and z z when n we prove here a list of arithmetic properties of z addition multiplication relation with integers when is a quadratic pisot vijayaraghavan unit quasicrystallographic inflation factors are particular examples we also consider the case of a cubic pisot vijayaraghavan unit associated with the seven fold cyclotomic ring at the end we show how the point sets are vertices of d dimensional tilings

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

mellin transforms and asymptotics digital sums abstract arithmetic functions related to number representation systems exhibit various periodicity phenomena for instance a well known theorem of delange expresses the total number of ones in the binary representations of the first n integers in terms of a periodic fractal function we show that such periodicity phenomena can be analyzed rather systematically using classical tools from analytic number theory namely the mellin perron formulae this approach yields naturally the fourier series involved in the expansions of a variety of digital sums related to number representation systems

balancedness and coboundaries in symbolic systems abstract this paper studies balancedness for infinite words and subshifts both for letters and factors balancedness is a measure of disorder that amounts to strong convergence properties for frequencies it measures the difference between the numbers of occurrences of a given word in factors of the same length we focus on two families of words namely dendric words and words generated by substitutions the family of dendric words includes sturmian and arnoux rauzy words as well as codings of regular interval exchanges we prove that dendric words are balanced on letters if and only if they are balanced on words in the substitutive case we stress the role played by the existence of coboundaries taking rational values and show simple criteria when frequencies take rational values for exhibiting imbalancedness

properties of words and recognizability of fixed points of a substitution resume soit u un mot infini non periodique point fixe d une substitution primitive nous montrons que pour n assez grand u ne contient aucune puissance n eme de mot nous donnons ensuite une condition necessaire et suffisante pour que soit reconnaissable au sens de host et queffelec et nous montrons qu ill suffit de bilateraliser cette definition pour obtenir une propriete verifiee cette fois par toutes les substitutions primitives a point fixe non periodique

power and exponential sums for generalized coding systems by a measure theoretic approach a measure theoretic approach to study the power and the exponential sums for the usual coding system has been developed since the 1990s in this paper we first introduce a new coding system and then give explicit formulas for the power and the exponential sums for the coding system by the measure theoretic approach an expression for the power sum using the generalized takagi function will also be given

joint spectral radius dilation equations and asymptotic behavior of radix rational sequences abstract radix rational sequences are solutions of systems of recurrence equations based on the radix representation of the index for each radix rational sequence with complex values we provide an asymptotic expansion essentially in the scale n log l n the precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence of first order differences the coefficients are holderian functions obtained through some dilation equations which are usual in the domains of wavelets and refinement schemes the proofs are ultimately based on elementary linear algebra

central sets and substitutive dynamical systems abstract in this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of pisot type central sets first introduced by furstenberg using notions from topological dynamics constitute a special class of subsets of n possessing strong combinatorial properties each central set contains arbitrarily long arithmetic progressions and solutions to all partition regular systems of homogeneous linear equations we give an equivalent reformulation of the strong coincidence condition in terms of central sets and minimal idempotent ultrafilters in the stone cech compactification n this provides a new arithmetical approach to an outstanding conjecture in tiling theory the pisot substitution conjecture the results in this paper rely on interactions between different areas of mathematics some of which had not previously been directly linked they include the general theory of combinatorics on words abstract numeration systems tilings topological dynamics and the algebraic topological properties of stone cech compactification of n

algorithm for determining pure pointedness of self affine tilings overlap coincidence in a self affine tiling in rd is equivalent to pure point dynamical spectrum of the tiling dynamical system we interpret the overlap coincidence in the setting of substitution delone set in rd and find an efficient algorithm to check the pure point dynamical spectrum this algorithm is easy to implement into a computer program we give the program and apply it to several examples in the course of the proof of the algorithm we show a variant of the conjecture of urbanski solomyak 2006 40 on the hausdorff dimension of the boundaries of fractal tiles

on the instability of equilibrium when the potential has a non strict local minimum instability is studied for a mechanical system with two degrees of freedom whose potential has a non strict local minimum at the origin under suitable conditions of smoothness it is shown that the corresponding equilibrium is unstable when the potential has a local minimum along a curve passing through the origin as a particular case we get instability if the potential is analytic and has a non isolated minimum at the origin these results improve those of g hamel 1 and silla 5 on the same subject

instability of a non isolated equilibrium in this paper non isolated equilibria of conservative mechanical systems are studied under mild non degeneracy conditions such equilibria are shown to be unstable in the sense of liapunov

balances for fixed points of primitive substitutions an infinite word defined over a finite alphabet a is balanced if for any pair of factors of the same length and for any letter a in the alphabet a a 1 where a denotes the number of occurrences of the letter a in the word in this paper we generalize this notion and introduce a measure of balance for an infinite sequence in the case of fixed points of primitive substitutions we show that the asymptotic behaviour of this measure is in part ruled by the spectrum of the incidence matrix associated with the substitution connections with frequencies of letters and other balance properties are also discussed

palindrome complexity we study the palindrome complexity of infinite sequences on finite alphabets i e the number of palindromic factors blocks of given length occurring in a given sequence we survey the known results and obtain new results for some sequences in particular for rote sequences and for fixed points of primitive morphisms of constant length belonging to class p of hof knill simon we also give an upper bound for the palindrome complexity of a sequence in terms of its block complexity

a condition of boshernitzan and uniform convergence in the multiplicative ergodic theorem this paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts if such a subshift satisfies a certain condition originally introduced by boshernitzan every locally constant sl 2 r valued cocycle is uniform as a consequence the corresponding schrodinger operators exhibit cantor spectrum of lebesgue measure zero an investigation of boshernitzan s condition then shows that these results cover all earlier results of this type and moreover provide various new ones in particular boshernitzan s condition is shown to hold for almost all circle maps and almost all arnoux rauzy subshifts

on the modulus of continuity for spectral measures in substitution dynamics abstract the paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weak mixing suspension flows over substitution automorphisms which yield information about the fractal structure of these measures the main results are first a holder estimate for the spectral measure of almost all suspension flows with a piecewise constant roof function second a log holder estimate for self similar suspension flows and third a holder asymptotic expansion of the spectral measure at zero for such flows our second result implies log holder estimates for the spectral measures of translation flows along stable foliations of pseudo anosov automorphisms a key technical tool in the proof of the second result is an arithmetic diophantine proposition which has other applications in appendix a this proposition is used to derive new decay estimates for the fourier transforms of bernoulli convolutions

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

a moment estimator for the index of an extreme value distribution on generalise l estimateur bien connu de hill de l indice d une fonction de reparatition avec queue de variation reguliere a une estimation de l indice d une loi de valeurs extremes on demontre la convergence et la normalite asymptotique on utilise l estimateur pour certaines estimations comme celle d une quantile elevee et d un point d extremite

languages d0l systems sets of curves and surface automorphisms we introduce extend and apply some relationships between formal language theory and surface theory first we show how boundaries of languages topologized with the cantor metric can be mapped to sets of curves on surfaces namely laminations second we present how and when endomorphisms of free monoids i e substitutions can be mapped to automorphisms of surfaces so that d0l systems correspond to iterations of these automorphisms third we apply these ideas to construct sets of non periodic irreducible automorphisms of surfaces following 14 35 43 so that the involved proofs do not use any differential or algebraic tools but accordingly substitution and d0l system theory of 11 12 31 32 37 mainly the decidability for a d0l language 12 to be strongly repetitive or not this construction also yields effective symbolic descriptions of the stable sets of curves associated with these automorphisms

on critical exponents in fixed points of non erasing morphisms let s be an alphabet of size t let f s s be a non erasing morphism let w be an infinite fixed point of f and let e w be the critical exponent of w we prove that if e w is finite then for a uniform f it is rational and for a non uniform f it lies in the field extension q r l 1 l where r l 1 l are the eigenvalues of the incidence matrix of f in particular e w is algebraic of degree at most t under certain conditions our proof implies an algorithm for computing e w