a conjecture concerning the hadamard product of inverses of m matrices abstract we conjecture that for an n n matrix a which is an inverse of an m matrix the hadamard product a a is also an inverse of an m matrix we have checked this conjecture without failure on many many examples but here we show that for quite a few well known classes of inverses of m matrices the conjecture is true it is known that the more general conjecture that when a and b are n n inverses of m matrices then a b is also an inverse of an m matrix is false however here too we are able to display some classes of inverses of m matrices which are closed under taking hadamard products

generic diffeomorphisms with superexponential growth of number of periodic orbits let m be a smooth compact manifold of dimension at least 2 and diff r m be the space of c r smooth diffeomorphisms of m associate to each diffeomorphism f 2 diff r m the sequence pn f of the number of isolated periodic points for f of period n in this paper we exhibit an open set n in the space of diffeomorphisms diff r m such for a baire generic diffeomorphism f 2 n the number of periodic points pnf grows with a period n faster than any following sequence of numbers fangn2zc along a subsequence i e pn f a ni for some ni 1 with i 1 in the cases of surface diffeomorphisms i e dim m d 2 an open set n with a supergrowth of the number of periodic points is a newhouse domain a proof of the man result is based on the gontchenko shilnikov turaev theorem gst a complete proof of that theorem is also presented

real bounds ergodicity and negative schwarzian for multimodal maps over the last 20 years many of the most spectacular results in the field of dynamical systems dealt specifically with interval and circle maps or perturbations and complex extensions of such maps primarily this is because in the one dimensional case much better distortion control can be obtained than for general dynamical systems however many of these spectacular results were obtained so far only for unimodal maps the aim of this paper is to provide all the tools for studying general multimodal maps of an interval or a circle by obtaining real bounds controlling the geometry of domains of certain first return maps and providing a new and we believe much simpler proof of absense of wandering intervals provided certain combinatorial conditions are satisfied large real bounds implying that certain first return maps are almost linear koebe distortion controlling the distortion of high iterates of the map and negative schwarzian derivative for certain return maps showing that the usual assumption of negative schwarzian derivative is unnecessary control of distortion of certain first return maps ergodic properties such as sharp bounds for the number of ergodic components

a two dimensional polynomial mapping with a wandering fatou component we show that there exist polynomial endomorphisms of 2 possessing a wandering fatou component these mappings are polynomial skew products and can be chosen to extend holomorphically of p 2 c we also find real examples with wandering domains in 2 the proof is based on parabolic implosion techniques and is based on an original idea of m lyubich

inverse m matrices ii this is an update of the 1981 survey by the first author in the meantime a considerable amount has been learned about the very special structure of the important class of inverse m matrices developments since the earlier survey are emphasized but we have tried to be somewhat complete and some results have not previously been published some proofs are given where appropriate and references are given for others after some elementary preliminaries results are grouped by certain natural categories

quadratic maps without asymptotic measure an interval map is said to have an asymptotic measure if the time averages of the iterates of lebesgue measure converge weakly we construct quadratic maps which have no asymptotic measure we also find examples of quadratic maps which have an asymptotic measure with very unexpected properties e g a map with the point mass on an unstable fix point as asymptotic measure the key to our construction is a new characterization of kneading sequences

nonexistence of wandering domains for strongly dissipative infinitely renormalizable henon maps at the boundary of chaos this article generalizes the nonexistence of wandering domains from unimodal maps to infinitely period doubling renormalizable henon like maps in the strongly dissipative area contracting regime this solves an open problem proposed by van strien discrete contin dyn syst 27 2 557 588 2010 and lyubich and martens invent math 186 1 115 189 2011 we partition the phase space of a henon like map into two regions the good region and the bad region the good region is where the method of proof for unimodal maps applies to henon like maps while the bad region is where serious difficulties occur these difficulties are resolved by the two row lemma an inequality that relates the contraction of areas to the contraction of bad regions after analyzing the competition of the two types of contraction we show that the case of bad regions happens at most finitely many times and complete the proof as an application the theorem enriches our understanding of the topological structure of the heteroclinic web the union of the stable manifolds of periodic orbits forms a dense set in the domain

matrices with a transitive graph and inverse m matrices abstract the relationship between inverse m matrices and matrices whose graph is transitive is studied the results are applied to obtain a new proof of the characterization due to m lewin and m neumann of 0 1 inverse m matrices

takens last problem and existence of non trivial wandering domains abstract in this paper we give an answer to a c r 2 r version of the open problem of takens in 42 which is related to historic behavior of dynamical systems to obtain the answer we show the existence of non trivial wandering domains near a homoclinic tangency which is conjectured by colli vargas 6 2 concretely speaking it is proved that any newhouse open set in the space of c r diffeomorphisms on a closed surface is contained in the closure of the set of diffeomorphisms which have non trivial wandering domains whose forward orbits have historic behavior moreover this result implies an answer in the c r category to one of the open problems of van strien 39 which is concerned with wandering domains for henon family

on inverse m matrices abstract we generalize a previous result of lewin and neumann and present a characterization of inverse m matrices the approach is mainly graph theoretical

how often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency abstract here we study an amazing phenomenon discovered by newhouse s newhouse non density of axiom a a on s 2 in proc sympos pure math vol 14 amer math soc 1970 pp 191 202 s newhouse diffeomorphisms with infinitely many sinks topology 13 1974 9 18 s newhouse the abundance of wild hyperbolic sets and nonsmooth stable sets of diffeomorphisms publ math inst hautes etudes sci 50 1979 101 151 it turns out that in the space of c r smooth diffeomorphisms diff r m of a compact surface m there is an open set u such that a baire generic diffeomorphism f u has infinitely many coexisting sinks in this paper we make a step towards understanding how often does a surface diffeomorphism have infinitely many sinks our main result roughly says that with probability one for any positive d a surface diffeomorphism has only finitely many localized sinks either of cyclicity bounded by d or those whose period is relatively large compared to its cyclicity it verifies a particular case of palis conjecture saying that even though diffeomorphisms with infinitely many coexisting sinks are baire generic they have probability zero one of the key points of the proof is an application of newton interpolation polynomials to study the dynamics initiated in v kaloshin b hunt a stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms i ann of math in press 92 pp v kaloshin a stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms ii preprint 85 pp

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

notes on inverse m matrices abstract we show that a nonsingular p by p matrix a is an inverse m matrix if and only if q t aq d is an n by n inverse m matrix whenever q is a p by n nonnegative matrix with exactly one positive entry in each column and d is a positive diagonal matrix this includes several facts about inverse m matrices as special cases we also show that a nonnegative n by n matrix a is in the closure of the inverse m matrices if and only if a d is nonsingular and a d 1 d 1 for each positive diagonal matrix d related results allow characterization of nilpotent matrices on the boundary of the inverse m matrices

complex variable hvpt complex variable hypervirial perturbation theory is applied to the case of oscillator and coulomb potentials perturbed by a single term potential of the form vxn or vrn respectively the trial calculations reported show that this approach can produce accurate complex energies for resonant states via a simple and speedy calculation and can also be useful in studies of pt symmetry and tunnelling resonance effects

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

inner product methods for eigenvalue calculations an inner product method of calculating eigenvalues is developed in both numerical and perturbation theoretic forms and shown to be applicable to bound state and resonant state problems the method is used to treat a problem in which the perturbed energy is a non analytic function of a perturbation parameter

existence and non existence of length averages for foliations since the pioneering work of ghys et al it has been known that several methods of dynamical systems theory can be adopted to study of foliations our aim in this paper is to investigate complexity of foliations by generalising existence problem of time averages in dynamical systems theory to foliations it has recently been realised that a positive lebesgue measure set of points without time averages only appears for complicated dynamical systems such as dynamical systems with heteroclinic connections or homoclinic tangencies in this paper we introduce the concept of length averages to singular foliations and attempt to collect interesting examples with without length averages in particular we demonstrate that length averages exist everywhere for any codimension one mathscr c 1 orientable singular foliation without degenerate singularities on a compact surface under a mild condition on quasi minimal sets of the foliation which is in strong contrast to time averages of surface flows

renormalization in the henon family ii the heteroclinic web we study highly dissipative henon maps f c b x y mapsto c x 2 by x with zero entropy they form a region in the parameter plane bounded on the left by the curve w of infinitely renormalizable maps we prove that morse smale maps are dense in but there exist infinitely many different topological types of such maps even away from w we also prove that in the infinitely renormalizable case the average jacobian bf on the attracting cantor set mathcal o f is a topological invariant these results come from the analysis of the heteroclinic web of the saddle periodic points based on the renormalization theory along these lines we show that the unstable manifolds of the periodic points form a lamination outside mathcal o f if and only if there are no heteroclinic tangencies

perturbation theory from moment recurrence relations moment recurrence relations are shown to be useful in perturbation calculations general equations are developed and different cases are discussed the anharmonic oscillator and zeeman effect in hydrogen are used as illustrative examples