rational surface maps with invariant meromorphic two forms let f s dashrightarrow s be a rational self map of a smooth complex projective surface s and eta be a meromorphic two form on s satisfying f eta delta eta for some delta in mathbf c we show that under a mild topological assumption on f there is a birational change of domain psi x dashrightarrow s such that psi eta has no zeros in this context we investigate the notion of algebraic stability for f proving that f can be made algebraically stable if and only if it acts nicely on the poles of eta we illustrate this last result in the case eta frac dx wedge dy xy where we translate our stability result into a condition on whether a circle homeomorphism associated to f has rational rotation number

the existence and asymptotic properties of a backfitting projection algorithm under weak conditions we derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function the procedure employs a recent projection interpretation of popular kernel estimators provided by mammen marron turlach and wand 1997 and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in bickel klaassen ritov and wellner 1993 our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components and in this sense improves on the method analysed in opsomer and ruppert 1997 we provide high level conditions independent of the sampling scheme we then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions

inference for a nonlinear counting process regression model martingale and counting process techniques are applied to the problem of inference for general conditional hazard functions this problem was first studied by beran who introduced a class of estimators for the conditional cumulative hazard and survival functions in the special case of time independent covariates here the covariate can be time dependent the classical i i d assumptions are relaxed by replacing them with certain asymptotic stability assumptions and models involving recurrent failures are included this is done within the framework of a general nonparametric counting process regression model important examples of the model include right censored survival data semi markov processes an illness death process with duration dependence and age dependent birth and death processes

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

one step local quasi likelihood estimation summary local quasi likelihood estimation is a useful extension of local least squares methods but its computational cost and algorithmic convergence problems make the procedure less appealing particularly when it is iteratively used in methods such as the back fitting algorithm cross validation and bootstrapping a one step local quasi likelihood estimator is introduced to overcome the computational drawbacks of the local quasi likelihood method we demonstrate that as long as the initial estimators are reasonably good the one step estimator has the same asymptotic behaviour as the local quasi likelihood method our simulation shows that the one step estimator performs at least as well as the local quasi likelihood method for a wide range of choices of bandwidths a data driven bandwidth selector is proposed for the one step estimator based on the pre asymptotic substitution method of fan and gijbels it is then demonstrated that the datadriven one step local quasi likelihood estimator performs as well as the maximum local quasilikelihood estimator by using the ideal optimal bandwidth

green currents for holomorphic automorphisms of compact kahler manifolds and some additional regularity properties very likely the currents t will describe the distribution of invariant manifolds of codimension s corresponding to the small est lyapounov exponents let dp denote the dynamical degree of order p of it describes the growth under iteration of the volume of p dimensional manifolds when d 1 it is natural to introduce first a positive closed 1 l current as ifnyoj 7 lim

hyperbolic polynomial diffeomorphisms of c2 ii hubbard trees this paper is a sequel to part i y ishii hyperbolic polynomial diffeomorphisms of i a non planar map adv math 218 2 2008 417 464 in the current article we construct an object analogous to a hubbard tree consisting of a pair of trees decorated with loops and a pair of maps between them for a hyperbolic polynomial diffeomorphism f of key notions in the construction are the pinching disks and the pinching locus which determine how local dynamical pieces are glued together to obtain a global picture it is proved that the shift map on the orbit space of a hubbard tree is topologically conjugate to f on its julia set several examples of hubbard trees are also given

cellular algebras and inverse semigroups abstract we show that under certain compatability assumptions the semigroup algebra of an inverse semigroup is cellular if the group algebras of its maximal subgroups are cellular motivating examples include the symmetric inverse semigroup also known as the rook monoid and the dual symmetric inverse semigroup

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

hecke algebras of finite type are cellular let mathcal h be the one parameter hecke algebra associated to a finite weyl group w defined over a ground ring in which bad primes for w are invertible using deep properties of the kazhdan lusztig basis of mathcal h and lusztig s a function we show that mathcal h has a natural cellular structure in the sense of graham and lehrer thus we obtain a general theory of specht modules for hecke algebras of finite type previously a general cellular structure was only known to exist in types an and bn

equational theories of semigroups with involution abstract we employ the techniques developed in an earlier paper to show that involutory semigroups arising in various contexts do not have a finite basis for their identities among these are partition semigroups endowed with their natural inverse involution including the full partition semigroup c n for n 2 the brauer semigroup b n for n 4 and the annular semigroup a n for n 4 n even or a prime power also all of these semigroups as well as the jones semigroup j n for n 4 turn out to be inherently nonfinitely based when equipped with another involution the skew one finally we show that similar techniques apply to the finite basis problem for existence varieties of locally inverse semigroups

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

estimating multiplicative and additive hazard functions by kernel methods we propose new procedures for estimating the component functions in both additive and multiplicativen onparametricm arker dependenht azard models we work with a full counting process framework that allows for left truncation and right censoring and time varying covariates our procedures are based on kernel hazard estimation as developed by nielsen and linton and on the idea of marginal integration we provide a central limit theorem for the marginal integration estimator we then define estimators based on finite step backfitting in both additive and multiplicative cases and prove that these estimators are asymptotically normal and have smaller variance than the marginal integration method

kernel estimation in a nonparametric marker dependent hazard model we introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker we establish the pointwise and global convergence of our estimator

nonsmooth backfitting for the excess risk additive regression model with two survival time scales we consider an extension of aalen s additive regression model allowing covariates to have effects that vary on two different time scales the two time scales considered are equal up to a constant that varies for each individual such as for example follow up time and age in medical studies or calendar time and age in longitudinal studies the model has been introduced in scheike 2001 where it was solved via smoothing techniques we present a new backfitting 20 algorithm estimating the structured model without having to use smoothing estimators of the cumulative regression functions on the two time scales are suggested by solving local estimating equations jointly on the two time scales we provide large sample properties and simultaneous confidence bands the model is applied to data on myocardial infarction providing a separation of the two effects stemming from time since diagnosis and age

fitting a bivariate additive model by local polynomial regression while the additive model is a popular nonparametric regression method many of its theoretical properties are not well understood especially when the backfitting algorithm is used for computation of the estimators this article explores those properties when the additive model is fitted by local polynomial regression sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed this model is shown to have the same rate of convergence as that of univariate local polynomial regression

exponential inequalities for martingales with application to maximum likelihood estimation for counting processes we obtain an exponential probability inequality for martingales and a uniform probability inequality for the process gdn where n is a counting process and where g varies within a class of predictable functions g for the latter we use techniques from empirical process theory the uniform inequality is shown to hold under certain entropy conditions on g as an application we consider rates of convergence for nonparametric maximum likelihood estimators for counting processes a similar result for discrete time observations is also presented

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 fatou bieberbach domains a fatou bieberbach domain is a domain in c2 which is a biholomorphic image of c2 and is not all of c2 the existence of such domains has been known for a long time there are several papers dealing with fatou bieberbach domains bf bs de e fs gl k n1 n2 rr1 rr2 s nevertheless they remain quite misterious objects and there are many open questions about them one of them is the following rr1 q 11 p 79 if is a fatoubieberbach domain and l is a complex line is it possible that a l is connected b l has finitely many components c l is a circular disc let be the open unit disc in c and let p suppose one wants to obtain a fatou bieberbach domain whose intersection with the z axis z 0 z c is approximately the unit disc one would try to find such that

dynamical compactifications of c 2 we find good dynamical compactifications for arbitrary polynomial mappings of c 2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula for maps of low topological degree we prove that the green function is well behaved for maps of maximum topological degree we give normal forms

hyperbolic polynomial diffeomorphisms of c2 iii iterated monodromy groups abstract this paper is a sequel to part i 13 and part ii 14 15 in the current article we relate several combinatorial descriptions of the julia sets for hyperbolic polynomial diffeomorphisms of c 2 quotients of solenoids 3 automata 22 and hubbard trees 14 15 the notion of iterated monodromy groups are defined for such diffeomorphisms and are used to construct automata from hubbard trees

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

hyperbolic polynomial diffeomorphisms of c2 i a non planar map abstract in this paper we develop a general framework for verifying hyperbolicity of holomorphic dynamical systems in c 2 our framework in particular enables us to construct the first example of a hyperbolic henon map of c 2 which is non planar i e which is not topologically conjugate on its julia set to a small perturbation of any expanding polynomial in one variable the key ideas in its proof are the poincare box which is a building block to apply our criterion for hyperbolicity an operation called fusion to merge two polynomials in one variable to obtain essentially two dimensional dynamics and rigorous computation by using interval arithmetic some conjectures and problems are also presented

dynamics of horizontal like maps in higher dimension we study the regularity of the green currents and of the equilibrium measure associated to a horizontal like map in under a natural assumption on the dynamical degrees we estimate the speed of convergence towards the green currents the decay of correlations for the equilibrium measure and the lyapounov exponents we show in particular that the equilibrium measure is hyperbolic we also show that the green currents are the unique invariant vertical and horizontal positive closed currents the results apply in particular to henon like maps to regular polynomial automorphisms of and to their small perturbations

stability and bifurcations for dissipative polynomial automorphisms of mathbb c 2 we study stability and bifurcations in holomorphic families of polynomial automorphisms of mathbb c 2 we say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there we first show that this defines a meaningful notion of stability which parallels in many ways the classical notion of j stability in one dimensional dynamics define the bifurcation locus to be the complement of the weak stability locus in the second part of the paper we prove that under an assumption of moderate dissipativity the parameters displaying homoclinic tangencies are dense in the bifurcation locus this confirms one of palis conjectures in the complex setting the proof relies on the formalism of semi parabolic bifurcation and the construction of critical points in semi parabolic basins which makes use of the classical denjoy carleman ahlfors and wiman theorems

pfaff systems currents and hulls let s be a pfaff system of dimension 1 on a compact complex manifold m we prove that there is a positive partial overline partial closed current t of bidimension 1 1 and of mass 1 directed by the pfaff system s there is no integrability assumption we also show that local singular solutions always exist under a transversality assumption of s on the boundary of an open set u we prove the existence in u of positive partial overline partial closed currents directed by s in u using i partial overline partial negative currents we discuss jensen measures local maximum principle and hulls with respect to a cone mathcal p of smooth functions in the euclidean complex space subharmonic in some directions the case where mathcal p is the cone of plurisubharmonic functions is classical we use the results to describe the harmonicity properties of the solutions of equations of homogeneous monge ampere type we also discuss extension problems of positive directed currents

regularity of dynamical green s functions for meromorphic maps of complex manifolds ergodic theory and pluripotential theory are closely related in nice enough situations dynamically defined green s functions give rise to invariant currents which intersect to yield measures of maximal entropy nice enough is often a condition on the regularity of the green s function in this paper we look at a variety of regularity properties that have been considered for dynamical green s functions we simplify and extend some known results and prove several others which are new we also give some examples indicating the limits of what one can hope to achieve in complex dynamics by relying solely on the regularity of a dynamical green s function

complex projective structures lyapunov exponent degree and harmonic measure we study several new invariants associated to a holomorphic projective struc ture on a riemann surface of finite analytic type the lyapunov exponent of its holonomy which is of probabilistic dynamical nature and was introduced in our previous work the degree which measures the asymptotic covering rate of the developing map and a family of harmonic measures on the riemann sphere previously introduced by hussenot we show that the degree and the lyapunov exponent are related by a simple formula and give estimates for the hausdorff dimension of the harmonic measures in terms of the lyapunov exponent in accordance with the famous sullivan dictionary this leads to a descrip tion of the space of such projective structures that is reminiscent of that of the space of polynomials in holomorphic dynamics

generators and relations for partition monoids and algebras abstract we investigate the manner in which the partition monoid p n and algebra p n may be presented by generators and relations making use of structural properties of p n as well as presentations for several key submonoids we obtain a number of presentations for p n including that given without a complete proof by halverson and ram in 2005 we then conclude by showing how each of these presentations gives rise to an algebra presentation for p n

miscellanea efficient estimation of additive nonparametric regression models summary we define a new procedure for estimating additive nonparametric regression models we use the integration method of linton nielsen 1995 to provide starting values that are then used in a one step backfitting procedure we show that our new method is efficient in a certain sense and dominates the straight integration method according to mean squared error

complex henon maps and discrete groups abstract consider the standard family of complex henon maps h x y p x a y x where p is a quadratic polynomial and a is a complex parameter let u be the set of points that escape to infinity under forward iterations the analytic structure of the escaping set u is well understood from previous work of j hubbard and r oberste vorth as a quotient of c d c by a discrete group of automorphisms isomorphic to z 1 2 z on the other hand the boundary j of u is a complicated fractal object on which the henon map behaves chaotically we show how to extend the group action to s 1 c in order to represent the set j as a quotient of s 1 c by an equivalence relation we analyze this extension for henon maps that are perturbations of hyperbolic polynomials with connected julia set or polynomials with a parabolic fixed point

heat equation and ergodic theorems for riemann surface laminations we study the dynamics of possibly singular foliations by riemann surfaces the main examples are holomorphic foliations by riemann surfaces in projective varieties we introduce the heat equation relative to a positive partial overline partial closed current and apply it to the directed currents associated with riemann surface laminations possibly with singularities this permits to construct the heat diffusion with respect to various laplacians that could be defined almost everywhere with respect to the partial overline partial closed current we prove two kinds of ergodic theorems for such currents one associated to the heat diffusion and one of geometric nature close to birkhoff s averaging on orbits of a dynamical system here the averaging is on hyperbolic leaves and the time is the hyperbolic time the heat diffusion theorem with respect to a harmonic measure is also developed for real laminations

global dynamics of quadratic second order difference equation in the first quadrant we investigate the global behavior of a quadratic second order difference equation x n 1 ax n 2 bx n x n 1 cx n 1 2 dx n ex n 1 f n 0 1 with non negative parameters and initial conditions we find the global behavior for all ranges of parameters and determine the basins of attraction of all equilibrium points

on commuting polynomial automorphisms of mathbb c k k 3 we characterize the polynomial automorphisms of mathbb c 3 which commute with a regular automorphism we use their meromorphic extension to mathbb p 3 and consider their dynamics on the hyperplane at infinity we conjecture the additional hypothesis under which the same characterization is true in all dimensions we give a partial answer to a question of s smale that in our context can be formulated as follows can any polynomial automorphism of mathbb c k be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer i e c f simeq mathbb z

semi parabolic bifurcations in complex dimension two parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena in this paper we consider the bifurcations of a holomorphic diffeomorphism in two complex dimensions with a semi parabolic semiattracting fixed point

dynamics of regular birational maps in p k abstract we develop the study of some spaces of currents of bidegree p p as an application we construct the equilibrium measure for a large class of birational maps of p k as intersection of green currents we show that these currents are extremal and that the corresponding measure is mixing

a structure theorem for semi parabolic henon maps abstract consider the parameter space p c 2 of complex henon maps h c a x y x 2 c a y a x a 0 which have a semi parabolic fixed point with one eigenvalue e 2 i p q in this paper we provide a complete topological description of the julia set and forward julia set within a family of semi parabolic henon maps i e those henon maps from the curve p which are perturbations of a quadratic polynomial p with a parabolic fixed point of multiplier we prove that there is an open disk of parameters in p for which the semi parabolic henon map has connected julia set j and is structurally stable on j and j the forward julia set j has a nice local description inside a certain bidisk it is a trivial fiber bundle over j p the julia set of the polynomial p with fibers biholomorphic to a disk the julia set j is homeomorphic to the quotient of a solenoid by an equivalence relation and j j the closure of the saddle periodic points

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

classification of recurrent domains for some holomorphic maps abstract riemann surface as in theorem 1 2 we show first that f is not constant on any component fl v l 0 hence we can assume using a diagonal process that for a subsequence fm fm h and h ld on ut of p c q g2 h q q consequently u of n is closed in t2 since fro ld on zn and since f is not of finite order see fm then f is conjugate to an irrational rotation on the riemann surface e we then show as in theorem 2 3 of fs3 that z is contained in f2 so e is closed in i2 the rest of the argument is as in theorem 1 2 or as in fs3 theorem 2 3 references b bbd bs cg fm fs1 fs2 fs3 fs4 g hi ko kr m in rr u beardon a iteration of rational functions springer verlag 1991 barrett d bedford e dadok j t actions on holomorphically separable complex manifolds math z 202 1989 65 82 bedford e smillie j polynomial diffeomorphisms of 2 ii amer j math 4 1991 657 679 carleson l gamelin t complex dynamics springer verlag 1993 friedland s milnor j dynamical properties of plane automorphisms ergodic theory and dynamical systems 9 1989 67 99 fornaess j e sibony n complex dynamics in higher dimension i asterisque 222 1994 201 231 fornaess j e sibony n complex dynamics in higher dimension ii to appear in ann math studies fornaess j e sibony n complex henon mappings in 2 and fatou bieberbach domains duke math j 65 1992 345 380 fornaess j e sibony n holomorphic dynamical systems to appear gavosto e to appear herman m recent results on some open questions on siegel s linearization kobayashi s hyperbolic manifolds and holomorphic mappings new york marcel dekker 1970 kruzhilin n g holomorphic automorphisms of hyperbolic reinhardt do mains math ussr izvestya 32 1989 15 38 milnor j dynamics in one complex variable introductory lectures suny stony brook institute for mathematical sciences preprint 1990 5 narashiman r several complex variables univ chicago press 1971 rosay j p rudin w holomorphic maps from ie n to c n tams 310 1988 47 86 ueda t fatou set in complex dynamics in projective spaces preprint

smoothed cox regression nonparametric regression was shown by beran and mckeague and utikal to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates we discuss application of kernel smoothing towards estimation in a generalized cox regression model with baseline intensity dependent on a covariate under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate root n and we also discuss estimation of the baseline cumulative hazard function and related parameters

smooth backfitting of proportional hazards with multiplicative components smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression by projecting the data down onto the structured space of interest smooth backfitting

the dimensionality reduction principle for generalized additive models soit x y une paire de variables aleatoires telles que x x 1 x j s etende sur c 0 1 j la distribution conditionnelle de y etant donne x x est supposee appartenir a une famille exponentielle appropriee ayant pour parametre r f x denote la dependance de vis a vis de x et f l approximation additive de f ayant la log vraisemblance esperee maximum possible

semiparametric analysis of general additive multiplicative hazard models for counting processes the additive multiplicative hazard model specifies that the hazard function for the counting process associated with a multidimensional covariate process z w t x t t takes the form of t z g 0 t w t 0 t h 0 t x t where 0 0 t 0 t t is a vector of unknown regression parameters g and h are known link functions and 0 is an unspecified baseline hazard function in this paper we develop a class of simple estimating functions for 0 which contains the partial likelihood score function in the special case of proportional hazards models the resulting estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions weak convergence of the aalen breslow type estimators for the cumulative baseline hazard function 0 t 0 t 0 u du is also established furthermore we construct adaptive estimators for 0 and o that achieve the semiparametric information bounds finally a real example is provided along with some simulation results

motzkin monoids and partial brauer monoids we study the partial brauer monoid and its planar submonoid the motzkin monoid we conduct a thorough investigation of the structure of both monoids providing information on normal forms green s relations regularity ideals idempotent generation minimal idempotent generating sets and so on we obtain necessary and sufficient conditions under which the ideals of these monoids are idempotent generated we find formulae for the rank smallest size of a generating set of each ideal and for the idempotent rank smallest size of an idempotent generating set of the idempotent generated subsemigroup of each ideal in particular when an ideal is idempotent generated the rank and idempotent rank are equal along the way we obtain a number of results of independent interest and we demonstrate the utility of the semigroup theoretic approach by applying our results to obtain new proofs of some important representation theoretic results concerning the corresponding diagram algebras the partial or rook brauer algebra and motzkin algebra