an extended fatou shishikura inequality and wandering branch continua for polynomials abstract let p be a polynomial of degree d with julia set j p let n be the number of non repelling cycles of p by the famous fatou shishikura inequality n d 1 the goal of the paper is to improve this bound the new count includes wandering collections of non pre critical branch continua i e collections of continua or points q i j p all of whose images are pairwise disjoint contain no critical points and contain the limit sets of eval q i 3 external rays also we relate individual cycles which are either non repelling or repelling with no periodic rays landing to individual critical points that are recurrent in a weak sense a weak version of the inequality reads n n irr i eval q i 2 d 1 where n irr counts repelling cycles with no periodic rays landing at points in the cycle q i form a wandering collection b c of non pre critical branch continua 1 if b c is non empty and 0 otherwise

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

extensions of positive definite integral kernels on the heisenberg group abstract we consider positive definite extensions of functions and distributions which are defined on a cylindrical neighborhood and positive definite in the heisenberg group when rotational invariance is assumed we show existence of p d extensions we also give formulas of the classical bochner type for all such extensions they are expanded in terms of an integral transform associated to the sub laplacian we further show that the p d extension problem is closely related to the theory of extensions of hermitian infinitesimal representations in the sense considered earlier by powers and fuglede these are extensions to integrable representations in generally larger so called dilation hilbert spaces

a structure theorem in one dimensional dynamics on considere la classe 7b a des applications c f 0 1 0 1 telles que f 0 f 1 0 et f a un unique point critique c 0 1 si le point critique de f 7b a est non plat alors f n a pas d intervalle errant

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

on the spectra of schrodinger operators we give two formulas for the lowest point open image in new window in the spectrum of the schrodinger operatorl d dt p d dt q where the coefficientsp andq are real valued bounded uniformly continuous functions on the real line we determine whether or not open image in new window is an eigenvalue forl in terms of a set of probability measures on the maximal ideal space of thec algebra generated by the translations ofp andq

the set of maps f_ ɑ b x x ɑ b 2π sin 2πx with any given rotation interval is contractible consider the two parameter family of real analytic maps f b x x b 2 sin 2 x which are lifts of degree one endomorphisms of the circle the purpose of this paper is to provide a proof that for any closed interval i the set of maps f b whose rotation interval is i form a contractible set

a method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programming abstract a method for computing global minima of real multivariate polynomials based on semidefinite programming was developed by n z shor j b lasserre and p a parrilo the aim of this article is to extend a variant of their method to noncommutative symmetric polynomials in variables x and y satisfying y x x y 1 and x x y y global minima of such polynomials are defined and showed to be equal to minima of the spectra of the corresponding differential operators we also discuss how to exploit sparsity and symmetry several numerical experiments are included the last section explains how our theory fits into the framework of noncommutative real algebraic geometry

dilations of symmetric operators shifted by a unitary group let q be a symmetric operator and ux a one parameter unitary group in a hilbert space such that ux dom q dom q and uxqux q x for dom q it is shown by a compactness argment that q admits a resolution q xf dx with a positive operator valued measure satisfying uxf ux f x this entails the existence of a selfadjoint extension of q to a larger space satisfying the analogus commutation relation with a suitable extended unitary group this result is generalized to n commuting symmetric operators transformed among each other by a representation of an amenable subgroup of the affine group in rn

estimation of a nonparametric censored regression model with an application to unemployment insurance spells in this paper we consider identification and estimation of a censored nonparametric location scale model we first show that in the case where the location function is strictly less than the fixed censoring point for all values in the support of the explanatory variables then the location function is not identified anywhere in contrast if the location function is greater or equal to the censoring point with positive probability then the location function is identified on the entire support including the region where the location function is below the censoring point in the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles the new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution a small scale simulation study indicates that the proposed estimation procedure performs well in finite samples we also present an empirical application to unemployment insurance duration using administrative level data from new jersey jel classification c14 c24 j64 j65

off diagonal terms in symmetric operators in this paper we provide a quantitative comparison of two obstructions for a given symmetric operator s with dense domain in hilbert space h to be self adjoint the first one is the pair of deficiency spaces of von neumann and the second one is of more recent vintage let p be a projection in h we say that it is smooth relative to s if its range is contained in the domain of s we say that smooth projections pi i 1 diagonalize s if a i pi spi 0 for all i and b supi pi i if such projections exist then s has a self adjoint closure i e s has a spectral resolution and so our second obstruction to self adjointness is defined from smooth projections pi with i pi spi 0 we prove results both in the case of a single operator s and a system of operators

positive elements in the algebra of the quantum moment problem let mathfrak a denote the extended weyl algebra mathfrak a 0 subset mathfrak a the weyl algebra it is well known that every element of mathfrak a of the forma b k b k is positive we prove that the converse implication also holds every positive elementa in mathfrak a has a quadratic sum factorization for some finite set of elements b k in mathfrak a the corresponding result is not true for the subalgebra mathfrak a 0 we identify states on mathfrak a 0 which do not extend to states on mathfrak a it follows from a result of powers and arveson that such states on mathfrak a 0 cannot be completely positive our theorem is based on a certain regularity property for the representations which are generated by states on mathfrak a and this property is not in general shared by representations generated by states defined only on the subalgebra mathfrak a 0

non commutative moment problems we are concerned with two problems called the generalized moment problem gmp and the quantum moment problem qmp both problems can be considered as non commutative versions of the classical moment problem et g be a connected lie group and 7b e g the universal enveloping algebra of the lie algebra of g suppose f is a given linear functional on 7b e g and is a fixed unitary representation of g we then ask gmp when do there exist a unitary representation u of g and a cyclic c vector for u such that f x x 7b e g qmp when is f of the form f x trdv x x 7b e g where is an operator such that dv x is of trace class for every x 7b e g

on quasisymmetry of quasiconformal mappings abstract suppose that f d d is a quasiconformal mapping where d and d are domains in r n and that d is a broad domain we show that for every arcwise connected subset a in d the weak quasisymmetry of the restriction f a a f a implies its quasisymmetry as a consequence we see that the answer to one of the open problems raised by heinonen from 1989 is affirmative under the additional condition that a is arcwise connected

rational maps with fatou components of arbitrarily large connectivity abstract we study the family of singular perturbations of blaschke products b a z z 3 z a 1 a z z 2 we analyse how the connectivity of the fatou components varies as we move continuously the parameter we prove that all possible escaping configurations of the critical point c a take place within the parameter space in particular we prove that there are maps b a which have fatou components of arbitrarily large finite connectivity within their dynamical planes

components of degree two hyperbolic rational maps we examine the structure of hyperbolic components and some boundary points of these for degree two rational maps rather than using quasi conformal deformation theory we use a technique from a theorem of thurston about the existence of rational maps this involves regarding a rational map as acting on the teichmuller space of punctured sphere

common limits of fibonacci circle maps we show that limits for the critical exponent tending to exist in both critical circle homeomorphism of golden mean rotation number and fibonacci circle coverings moreover they are the same the limit map is not analytic at the critical point which is flat but has non trivial complex dynamics

factoring the logarithmic spiral distortion of length and angle are widely studied in geometry and dynamics much of the success in the study of one dimensional complex dynamics flow from the ahlfors bers sullivan a b s 1 theory for deforming conformal structures essentially from the existence and uniqueness theory for the beltrami equation d f d f no comparable analytic theory exists for the distortion of length in the plane or of length or angle in higher dimensions in these cases the local distortion is specified by more than d parameters in dimension d so the analogous equations are over determined what exists instead is a coarser more topological discussion initiated by sullivan of structures extension and isotopy of imbeddings s 2 t v in the quasiconformal and bilipschitz quasi isometric categories the coarseness is the use of the alexander isotopy which crushes rather than unwinds homeomorphisms in this paper we find a constraint on the more delicate method of returning a quasi isometry to the identity factorization into maps of small isometric distortion we study the following l quasi isometry of the closed unit disk a xl x2 x 2 x2 1