thermodynamics dimension and the weil petersson metric in this paper we study branched coverings of metrized simplicial trees f t t which arise from polynomial maps f c c with disconnected julia sets we show that the collection of all such trees up to scale forms a contractible space ptd compactifying the moduli space of polynomials of degree d that f records the asymptotic behavior of the multipliers of f and that any meromorphic family of polynomials over can be completed by a unique tree at its central fiber in the cubic case we give a combinatorial enumeration of the trees that arise and show that pt3 is itself a tree resume dans ce travail nous etudions des revetements ramifies d arbres metriques simpliciaux f t t qui sont obtenus a partir d applications polynomiales f c c possedant un ensemble de julia non connexe nous montrons que la collection de tous ces arbres a un facteur d echelle pres forme un espace contractile ptd qui compactifier l espace des modules des polynomes de degre d nous montrons aussi que f enrigistre le comportement asymptotique des multiplicateurs de f et que tout famille meromorphe de polynomes definis sur peut etre completee par un unique arbre comme sa fibre centrale dans le cas cubique nous donnons une enumeration combinatoire des arbres ainsi obtenus et montrons que pt3 est lui meme un arbre

on the algebraic structure of quasi cyclic codes iii generator theory following parts i and ii quasi cyclic codes of given index are studied as codes over a finite polynomial ring these latter codes are decomposed by the chinese remainder theorem crt or equivalently the mattson solomon transform into products of shorter codes over larger alphabets we characterize and enumerate self dual one generator quasi cyclic codes in that context we give an algorithm to remove some equivalent codes from that enumeration a generalization to multigenerator codes is sketched

a family of highly symmetric codes we define a class of codes admitting a large automorphism group this family contains the binary extended hamming code the hexacode the golay codes the pless symmetry codes as well as the 16 4 12 sub 8 codes constructed by marcugini et al a computer search resulted in the construction of codes with new parameters 28 7 18 sub 8 32 8 20 sub 8 and 39 13 17 sub 4 belonging to this family

self bumping of deformation spaces of hyperbolic 3 manifolds let n be a hyperbolic 3 manifold and b a component of the interior of ah 1 n the space of marked hyperbolic 3 manifolds homotopy equivalent to n we will give topological conditions on n sufficient to give b such that for every sufficiently small neighbourhood v of v b is disconnected this implies that b is not a manifold with boundary

a class of linear codes with good parameters a construction of linear codes with good parameters is given based on brouwer s table more than 100 new codes are obtained from our construction

new binary linear codes from algebraic curves many new binary linear codes compared with brouwer s 2000 table are found from a construction based on algebraic curves over finite fields

towards a semiclassical theory of the quantum baker s map abstract we develop semiclassical 0 treatments of the quantum baker s map paying special attention to a the discrete and finite nature of its hilbert space and b the asymptotic analysis of the true quantum objects themselves new techniques are described at the theoretical level exact symbolic decomposition of the propagator and at the numerical level color graphics display of operators in the kirkwood representation both of which are of general interest for other quantized chaotic maps periodic orbit theory is tested numerically and we find that log corrections need to be included before an accurate calculation of the spectrum from periodic orbits can be achieved however the asymptotic analysis of the traces of the propagator reveals unexpected departures from standard semiclassical theory those anomalies which we compute explicitly in a few cases are traced ultimately to the discontinuity of the map and to the compactness of the phase space the analysis is far from complete but the results point towards the necessity of careful assessment of semiclassical folklore when applied to chaotic maps

quantum maps from transfer operators abstract the selberg zeta function s s yields an exact relationship between the periodic orbits of a fully chaotic hamiltonian system the geodesic flow on surfaces of constant negative curvature and the corresponding quantum system the spectrum of the laplace beltrami operator on the same manifold it was found that for certain manifolds s s can be exactly ewritten as the fredholm grothendieck determinant det 1 t s where ts is a generalization of the ruelle perron frobenius transfer operator we present an alternative derivation of this result yielding a method to find not only the spectrum but also the eigenfunctions of the laplace beltrami operator in terms of eigenfunctions of ts various properties of the transfer operator are investigated both analytically and numerically for several systems

random walks kleinian groups and bifurcation currents let be a holomorphic family of representations of a finitely generated group g into psl 2 parameterized by a complex manifold we define a notion of bifurcation current in this context that is a positive closed current on describing the bifurcations of this family of representations in a quantitative sense it is the analogue of the bifurcation current introduced by demarco for holomorphic families of rational mappings on 1 our definition relies on the theory of random products of matrices so it depends on the choice of a probability measure on g

non realizability and ending laminations proof of the density conjecture we give a complete proof of the bers sullivan thurston density conjecture in the light of the ending lamination theorem it suffices to prove that any collection of possible ending invariants is realized by some algebraic limit of geometrically finite hyperbolic manifolds the ending invariants are either riemann surfaces or filling laminations supporting masur domain measured laminations and satisfying some mild additional conditions with any set of ending invariants we associate a sequence of geometrically finite hyperbolic manifolds and prove that this sequence has a convergent subsequence we derive the necessary compactness theorem combining the rips machine with non existence results for certain small actions on real trees of free products of surface groups and free groups we prove then that the obtained algebraic limit has the desired conformal boundaries and the property that none of the filling laminations is realized by a pleated surface in order to be able to apply the ending lamination theorem we have to prove that this algebraic limit has the desired topological type and that these non realized laminations are ending laminations that this is the case is the main novel technical result of this paper loosely speaking we show that a filling masur domain lamination which is not realized is an ending lamination

the bandwidth minimization problem for cyclic caterpillars with hair length 1 is np complete in this paper we show that the bandwidth minimization problem remains np complete for cyclic caterpillars with hair length 1 cyclic caterpillars with hair length 1 are graphs in which the removal of all pendant vertices results in a simple cycle

julia fatou sullivan theory for real one dimensional dynamics our aim is to show that the julia fatou sullivan structure theory for the dynamics of rational maps is also valid for smooth endomorphisms of the circle and of the interval under extremely mild smoothness and non flatness conditions in order to stress the similarity between real and complex one dimensional dynamics let us recall the main results from the fatou julia sullivan theory if f is a rational map then there is a dynamical decomposition of the riemann sphere into the disjoint union of two totally invariant i e both forward and backward invariant sets j f f f here f f is the domain of normality of the family of iterates of f and is called the fatou set its complement which is called the julia set off is a compact set which contains all the complications of the dynamics off the connected components of the open set f f are mapped onto each other by f hence the orbit of a component of f f is the union of some components of f f julia proved in the beginning of the century that if a component of f f is periodic and contains an attracting periodic point then the orbit of this component must contain a critical point sullivan in the remarkable paper su showed via quasi conformal deformations that the components are eventually periodic and fall into finitely many orbits let n be either the circle s j or a compact interval of the real line and f n n be a smooth endomorphism a critical point of f is a point where the derivative vanishes a critical point is non flat if some higher derivative is non zero a critical point is an inflection point if it has a neighbourhood where f is monotone otherwise it is called a turning point assume f is not a homeomorphism i f f is a homeomorphism then these maps correspond to degree 1 rational maps of the riemann sphere and the situation is

multiple bumping of components of deformation spaces of hyperbolic 3 manifolds let m be a hyperbolizable 3 manifold with nonempty incompressible boundary of negative euler characteristic suppose that b 1 b k is a collection of components of the interior of the space of complete marked hyperbolic 3 manifolds homotopy equivalent to m such that for any i j inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we prove that there is a geometrically finite hyperbolic structure on int m which is in the closure of each b i moreover we show that this structure can be constructed so as to admit quasiconformal deformations which also lie in the closure of every b i

on continuous extensions of grafting maps the definition of the grafting operation for quasifuchsian groups is extended by bromberg preprint to all b groups in this paper we show that the extended grafting maps behave as continuous maps for every sequence which converges standardly to a boundary group although the maps are not continuous in general as a consequence of this result we extend goldman s grafting theorem for quasifuchsian groups to all boundary b groups

a class of polynomial codes we present a construction of linear codes from polynomials it turns out that some new codes are obtained from our construction and improve parameters of brouwer s table

ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic 3 manifolds we show that geometrically finite kleinian groups are dense in the boundary of the quasiconformal deformation space of any geometrically finite kleinian group

finding the minimum bandwidth of an interval graph abstract an assignment of unique integers to the vertices of a graph is called a linear layout the bandwidth minimization problem bandwidth is the following given a graph g v e and an integer k determine whether there exists a linear layout of g such that the maximum difference between adjacent vertices is bounded by k interval graphs are the intersection graphs of a family of intervals of the real line bandwidth remains np complete even when restricted to special subclasses of trees we show that bandwidth can be solved in time o n2 for interval graphs moreover for a given interval graph a linear layout with minimum bandwidth can be constructed in time o n2logn as a by product we get that this construction can be done for proper interval graphs in time o nlog n m

symbolic dynamics for geodesic floes the subject of symbolic dynamics is of central importance in the modern theory of dynamical systems the use of symbolic sequences to study dynamical properties of geodesies originates in the work of koebe 21 22 and morse 24 25 and is already foreshadowed in hadamard 15 and jordan 19 the method of koebe and of morse is to code a geodesic on a surface m of negative curvature by recording the order in which it traverses a given set of labelled curves on m the treatment of morse allows variable curvature but assumes at least two boundary components whereas koebe assumes constant curvature but allows infinite connectivity and nonorientability and treats the more difficult case of a closed surface this last case is handled by recording crossings of a fixed pants decomposition anticipating the thurston parameterization of simple curves as described in 11 both koebe and morse used their codings to demonstrate the existence of countably many closed geodesies and of everywhere dense transitive geodesies morse further constructed the first nonsynthetic example of a recurrent nonperiodic discontinuous motion in modern terminology a minimal nowhere dense set later 26 morse treated the special closed surfaces of genus g associated to tesselations of the disc d by regular 4 gons each edge of a region in such a tesselation may be labelled by the isometry which glues it to another side of the same region in forming the quotient sin face m the set of isometries appearing as labels generate tti m thus any geodesic is coded as a doubly infinite sequence of generators of iri m the same method applies quite generally to tesselations associated to any fuchsian group we call the sequences thus obtained cutting sequences and refer to generating sets of this kind as geometric the difficulty of course is to determine precisely the class of sequences which occur for a surface with boundary one obtains exactly reduced sequences in the generators in generalthe problem4s gompligated1 henge the difficulties encountered in 26 see also theorem 3 below there is another method of coding geodesies using certain boundary expansions for points at infinity in the universal cover of m for the modular surface h sl 2 2 the appropriate expansions are continued fractions and for the symmetrical genus g surfaces above they are the nielsen boundary expansions of 27

intertwining the geodesic flow and the schrodinger group on hyperbolic surfaces we construct an explicit intertwining operator mathcal l between the schrodinger group e it frac triangle2 and the geodesic flow on certain hilbert spaces of symbols on the cotangent bundle t x of a compact hyperbolic surface x d we also define invariant eigendistributions of the geodesic flow ps j k nu j nu k patterson sullivan distributions out of pairs of triangle eigenfunctions generalizing the diagonal case j k treated in anantharaman and zelditch ann henri poincare 8 2 361 426 2007 the operator mathcal l maps ps j k nu j nu k to the wigner distribution w gamma j k studied in quantum chaos we define hilbert spaces mathcal h ps whose dual is spanned by ps j k nu j nu k resp mathcal h w whose dual is spanned by w gamma j k and show that mathcal l is a unitary isomorphism from mathcal h w to mathcal h ps

slicing skinning and grafting we prove that a bers slice is never algebraic meaning that its zariski closure in the character variety has strictly larger dimension a corollary is that skinning maps are never constant the proof uses grafting and the theory of complex projective structures

prym varieties and teichmuller curves this paper gives a uniform construction of infinitely many primitive teichmuller curves v mg for g 2 3 and 4

quasiconformal homeomorphisms and dynamics ii structural stability implies hyperbolicity for kleinian groups sous groupe de psl 2 c familles holomorphes d homeomorphismes de c lemme champs de ligne invariants familles holomorphes de groupes abstraitement isomorphes car finiment genere la stabilite structurelle implique geometriquement fini ou rigide theoreme a avec paraboles stabilite structurelle au sens de la dynamique differentiable

on the discreteness criterion in sl 2 c in tukia and wang math scand 91 214 220 2002 the authors conjectured that a non elementary subgroup in sl 2 c containing parabolic and elliptic elements is discrete if and only if each two generator subgroup generated by a parabolic and an elliptic element is discrete the purpose of this paper is to give an affirmative answer to this question

on the density of geometrically finite kleinian groups the density conjecture of bers sullivan and thurston predicts that each complete hyperbolic 3 manifold m with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3 manifolds we prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends

construction of global function fields from linear codes and vice versa we introduce a new connection between linear codes and global function fields which in turn allows us to construct new global function fields with improved lower bounds on the number of rational places the genus and number of rational places of subfields of certain families of cyclotomic function fields are given as well

quantum codes derived from certain classes of polynomials one central theme in quantum error correction is to construct quantum codes that have a relatively large minimum distance in this paper we first present a construction of classical linear codes based on certain classes of polynomials through these classical linear codes we are able to obtain some new quantum codes it turns out that some of the quantum codes exhibited here have better parameters than the ones available in the literature

area distortion of quasiconformal mappings in recent years quasiconformal mappings have been an efficient tool in the study of dynamical systems of the complex plane we show here that in turn methods or ideas from dynamical systems can be used to solve a number of open questions in the theory of planar quasiconformal mappings it has been known since the work of ahlfors a and mori mo that k quasiconformal mappings are locally h51der continuous with exponent 1 k the function

on finding the minimum bandwidth of interval graphs abstract let g v e be an interval graph with v n and e m an o n 2 log n algorithm was proposed in kratsch inform comput 74 140 158 1987 to find the bandwidth of g we show that this algorithm is wrong and provide a corrected version of the same also it was observed in 4 that the bandwidth of a proper interval graph can be computed in o n log n m time we show how this idea can be modified slightly to yield an o n m algorithm

some applications of thermodynamic formalism to manifolds with constant negative curvature the purpose of this article is to present a different approach to the analysis of the spectrum of a compact surface of constant negative curvature to explain our ideas we recall that there exists a highly successful theory for analyzing zeta functions for closed geodesics originated by a selberg the zeros for this zeta function identify the eigenvalues of the laplacian for the surface the main tool in this analysis is the selberg trace formula 7 there exists an approach having its roots in ergodic theory and statistical mechanics for analyzing zeta functions for geodesic and more general flows the principle here is quite different from that in the selberg approach the zeta function is some form of determinant of a family of perron frobenius type operators parameterized by the complex domain the zeta function behaves like a determinant in that zeros correspond to parameters for which the corresponding operator is not invertible 10 111 since both methods apply to surfaces of constant negative curvature this suggests that there is some mechanism involving a perron frobenius type operator characterizing the laplacian spectrum of the surface 161 oooi 8708 91 7 50

good linear codes from polynomial evaluations in the present paper we generalize the ideas of code constructions from our previous papers it turns out that the codes in the previous papers can be viewed as special cases of those in this paper moreover our constructions produce some good codes in terms of their parameters in particular some best known codes can be obtained through our methods furthermore our constructions are explicit and the codes can be easily implemented as shown in the tables of appendix besides one new code i e a 4 ary 64 15 31 linear code is found through our constructions

a thermodynamic formalism approach to the selberg zeta function for hecke triangle surfaces of infinite area we provide an explicit construction of a cross section for the geodesic flow on infinite area hecke triangle surfaces which allows us to conduct a transfer operator approach to the selberg zeta function further we construct closely related cross sections for the billiard flow on the associated triangle surfaces and endow the arising discrete dynamical systems and transfer operator families with two weight functions which presumably encode dirichlet respectively neumann boundary conditions the fredholm determinants of these transfer operator families constitute dynamical zeta functions which provide a factorization of the selberg zeta function of the hecke triangle surfaces

the selberg zeta function for convex co compact schottky groups we give a new upper bound on the selberg zeta function for a convex co compact schottky group acting on the hyperbolic space n 1 in strips parallel to the imaginary axis the zeta function is bounded by exp c s where is the dimension of the limit set of the group this bound is more precise than the optimal global bound exp c s n 1 and it gives new bounds on the number of resonances scattering poles of n 1 the proof of this result is based on the application of holomorphic l2 techniques to the study of the determinants of the ruelle transfer operators and on the quasi self similarity of limit sets we also study this problem numerically and provide evidence that the bound may be optimal our motivation comes from molecular dynamics and we consider n 1 as the simplest model of quantum chaotic scattering

a class of linear codes with good parameters from algebraic curves a class of linear codes with good parameters is constructed in this correspondence it turns out that linear codes of this class are subcodes of the subfield subcodes of goppa s geometry codes in particular we find 61 improvements on brouwer s table based on our codes

density and location of resonances for convex co compact hyperbolic surfaces let x vargamma backslash mathbb h 2 be a convex co compact hyperbolic surface and let be the hausdorff dimension of the limit set let x be the hyperbolic laplacian we show that the density of resonances of the laplacian x in rectangles bigl sigma leq mathrm re s leq delta big vert mathrm im s big vert leq t bigr is less than o t1 in the limit t where frac delta 2 this improves the previous fractal weyl upper bound of zworski invent math 136 2 353 409 1999 and goes in the direction of a conjecture stated in jakobson and naud geom funct anal 22 2 352 368 2012