bluuebunny/crossref_metadata_2025_split huggingface dataset:
Un théorème de préparation pour fonctions à développement Tchébychévien
Authors: Joyal Pierre 
Published: September 2008

AbstractIn this article, we prove a preparation theorem for functions which admit a certain type of expansion called Chebychev expansion. Taylor expansions are particular cases of Chebychev expansions. The result is based on an approach essentially different from those used for the classical preparation theorems. It has applications in bifurcation theory of vector fields.
Rational functions with no recurrent critical points
Authors: Urbański Mariusz 
Published: September 2008

AbstractLet h be the Hausdorff dimension of the Julia set of a rational map with no nonperiodic recurrent critical points. We give necessary and sufficient conditions for h-dimensional Hausdorff measure and h-dimensional packing measure of the Julia set to be positive and finite. We also show that either the Julia set is the whole Riemann sphere or h < 2 and that if a rational map (not necessarily with no nonperiodic recurrent critical points!) has a rationally indifferent periodic point, then h > 1/2.
Polynomial beta functions
Authors: Angelis Valerio De 
Published: September 2008

AbstractThe pointwise spectral radii of irreducible matrices whose entries are polynomials with positive, integral coefficients are studied in this paper. Most results are derived in the case that the resulting algebraic function, the beta function of S. Tuncel, is in fact a polynomial. We show that the set of beta functions forms a semiring, and the spectral radius of a matrix of beta functions is again a beta function. We also show that the coefficients of a polynomial beta function p must be real algebraic integers, and p satisfies (after a change of variables if necessary) the inequality for non-zero (and not all positive) complex numbers z1,…,zd. If and the ordered sequence of exponents appearing in p is of the form (m,m+1,…,M−,1,M) for some integers m and M, the same inequality is necessary and sufficient for p to be a beta function.
Regularity at infinity of compact negatively curved manifolds
Authors: Hamenstädt Ursula 
Published: September 2008

AbstractIt is shown that three different notions of regularity for the stable foliation on the unit tangent bundle of a compact manifold of negative curvature are equivalent. Moreover if is a time-preserving conjugacy of geodesic flows of such manifolds M, N then the Lyapunov exponents at corresponding periodic points of the flows coincide. In particular Δ also preserves the Lebesgue measure class.
Entropy, transverse entropy and partitions of unity
Authors: Langevin Rémi , Walczak Pawel G. 
Published: September 2008

AbstractThe topological entropy of a transformation is expressed in terms of partitions of unity. The transverse entropy of a flow tangential to a foliation is defined and expresed in a similar way. The geometric entropy of a foliation of a Riemannian manifold is compared with the transverse entropy of its geodesic flow.
Equivalence of boundary measures on covering trees of finite graphs
Authors: Lyons Russell 
Published: September 2008

AbstractLet T be the universal covering tree of a finite graph, G. By analogy with an open problem concerning negatively curved covering manifolds, Kaimanovich asked when two of the three natural measure classes on ∂T can coincide, the three measures being harmonic measure, the Patterson measure, and visibility measure. We provide an almost complete answer and discuss related issues. The answer is quite surprising in some cases.
An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps
Authors: Baladi V. , Ruelle D. 
Published: September 2008

AbstractWe consider a piecewise continuous, piecewise monotone interval map and a piecewise constant weight. With these data we associate a weighted kneading matrix which generalizes the Milnor—Thurston matrix. We show that the determinant of this matrix is related to a natural weighted zeta function.
Falconer's formula for the Hausdorff dimension of a self-affine set in R2
Authors: Hueter Irene , Lalley Steven P. 
Published: September 2008

Let A1, A2,…,Ak be a finite set of contractive, affine, invertible self-mappings of R2. A compact subset Λ of R2 is said to be self-affine with affinitiesA1, A2,…,Ak ifIt is known [8] that for any such set of contractive affine mappings there is a unique (compact) SA set with these affinities. When the affine mappings A1, A2,…,Ak are similarity transformations, the set Λ is said to be self-similar. Self-similar sets are well understood, at least when the images Ai(Λ) have ‘small’ overlap: there is a simple and explicit formula for the Hausdorff and box dimensions [12, 10]; these are always equal; and the δ-dimensional Hausdorff measure of such a set (where δ is the Hausdorff dimension) is always positive and finite.
On the integrability of intermediate distributions for Anosov diffeomorphisms
Authors: Jiang M. , Pesin Ya B. , de la Llave R. 
Published: September 2008

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.
Anosov automorphisms for nilmanifolds and rigidity of group actions
Authors: Qian Nantian 
Published: September 2008

AbstractWe obtain the density of Lyapunov exponents for maximal abelian ℝ-split group in kth tensor product representation of a subgroup Γ ⊂ SL(n, ℤ) of finite index under certain conditions. Anosov and Cartan actions of such groups associated with irreducible representations of SL(n, ℝ) are also classified. Examples of rigidity of actions on nilmanifolds are discussed.
Ensembles invariants des flots géodésiques des variétés localement symétriques
Authors: Zeghib A. 
Published: September 2008

AbstractWe study the rectifiable invariant subsets of algebraic dynamical systems determined by ℝ-semisimple one parameter groups. We show that their ergodic components are algebraic. A more precise geometric description of these components is possible in some cases of geodesic flows of locally symmetric spaces with non-positive curvature.
A topological invariant for volume preserving diffeomorphisms
Authors: Gambaudo Jean-Marc , Pécou Elisabeth 
Published: September 2008

AbstractFor a smooth diffeomorphism f in ℝn+2, which possesses an invariant n-torus , such that the restriction f is topologically conjugate to an irrational rotation, we define a number which represents the way the normal bundle to the torus asymptotically wraps around . We prove that this number is a topological invariant among volume-preserving maps. This result can be seen as a generalization of a theorem by Naishul, for which we give a simple proof.
Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure
Authors: Lyons Russell , Pemantle Robin , Peres Yuval 
Published: September 2008

AbstractWe consider simple random walk on the family treeTof a nondegenerate supercritical Galton—Watson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary ofT. Concretely, this implies that an exponentially small fraction of thenth level ofTcarries most of the harmonic measure. First-order asymptotics for the rate of escape, Green function and the Avez entropy of the random walk are also determined. Ergodic theory of the shift on the space of random walk paths on trees is the main tool; the key observation is that iterating the transformation induced from this shift to the subset of ‘exit points’ yields a nonintersecting path sampled from harmonic measure.
Ergodic properties of a dynamical system arising from percolation theory
Authors: Kraaikamp Cor , Meester Ronald 
Published: September 2008

AbstractWe consider the following dynamical system: take a d-dimensional real vectorwith positive coordinates. Now keep the smallest coordinate and subtract this one from the others, and iterate this process. When the starting vector is x we denote by xn the result after n iterations. It is shown that for almost all x, limn→∞xn ≠ 0 (the null vector). This is shown to be equivalent to the conjectured finiteness of an algorithm which produces the critical probability in a certain dependent percolation model.
On the sofic limit sets of cellular automata
Authors: Maass Alejandro 
Published: September 2008

AbstractIt is not known in general whether any mixing sofic system is the limit set of some one-dimensional cellular automaton. We address two aspects of this question. We prove first that any mixing almost of finite type (AFT) sofic system with a receptive fixed point is the limit set of a cellular automaton, under which it is attained in finite time. The AFT condition is not necessary: we also give examples of non-AFT sofic systems having the same properties. Finally, we show that near Markov sofic systems (a subclass of AFT sofic systems) cannot be obtained as limit sets of cellular automata at infinity.
Square functions in ergodic theory
Authors: Jones Roger L. , Ostrovskii Iosif V. , Rosenblatt Joseph M. 
Published: September 2008

AbstractGiven the usual averages in ergodic theory, let n1 ≤ n2 ≤ … and . There is a strong inequality ‖Sf‖2 ≤ 25‖f‖2 and there is a weak inequality m{Sf > λ} ≤ (7000/λ)‖f‖1. Related results and questions for other variants of this square function are also discussed.
Measures of full dimension on affine-invariant sets
Authors: Kenyon R. , Peres Y. 
Published: September 2008

AbstractWe determine the Hausdorff and Minkowski dimensions of some self-affine Sierpinski sponges, extending results of McMullen and Bedford. This result is used to show that every compact set invariant under an expanding toral endomorphism which is a direct sum of conformal endomorphisms supports an invariant measure of full dimension.
Reidemeister torsion and Morse–Smale flows
Authors: Sánchez-Morgado Héctor 
Published: September 2008

AbstractFor several types of stable flows φ and representations ρ of the fundamental group of the underlying manifold, R-torsion for ρ can be computed from the periodic orbits of φ. However, there are counterexamples and the purpose of this paper is to describe the role of heteroclinic orbits in such counterexamples.
Expansive homeomorphisms and hyperbolic diffeomorphisms on 3-manifolds
Authors: Vieitez José L. 
Published: September 2008

AbstractThis paper is a contribution to the classification problem of expansive homeomorphisms. Let M be a compact connected oriented three dimensional topological manifold without boundary and f: M → M an expansive homeomorphism.We show that if the topologically hyperbolic period points of f are dense in M then M = , and f is conjugate to an Anosov diffeomorphism. This follows from our basic result: for such a homeomorphism, all stable and unstable sets are (tamely embedded) topological manifolds.
Minimal entropy and Mostow's rigidity theorems
Authors: Besson Gérard , Courtois Gilles , Gallot Sylvestre 
Published: September 2008

Let (Y, g) be a compact connectedn-dimensional Riemannian manifold and let () be its universal cover endowed with the pulled-back metric. Ify∈, we definewhereB(y,R) denotes the ball of radiusRaroundyin. It is a well known fact that this limit exists and does not depend ony([Man]). The invarianth(g) is called the volume entropy of the metricgbut, for the sake of simplicity, we shall use the term entropy. The idea of recognizing special metrics in terms of this invariant looks at first glance very optimistic. First the entropy, which behaves like the inverse of a distance, is sensitive to changes of scale which makes it a bad invariant: however, this is a minor drawback that can be circumvented by looking at the behaviour of the entropy functional on the space of metrics with fixed volume (equal to one for example). Nevertheless, it seems very unlikely that two numbers, the entropy and the volume, might characterize any metric. The very first person to consider such a possibility was Katok ([Kat1]). In this article the entropy is thought of as a dynamical invariant which actually is suggested by its name. More precisely, let us define this dynamical invariant, which is called the topological entropy: let (M,d) be a compact metric space and ψt, a flow on it, we define.
Fixed points of elliptic reversible transformations with integrals
Authors: Gong Xianghong 
Published: September 2008

AbstractWe show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general reversible transformation with integrals. We also study the integrable holomorphic reversible transformations coming from real analytic surfaces in ℂ2 with non-degenerate complex tangents. We show the existence of real analytic surfaces with hyperbolic complex tangents, which are contained in a real hyperplane, but cannot be transformed into the Moser—Webster normal form through any holomorphic transformation.
Estimating invariant measures and Lyapunov exponents
Authors: Hunt Brian R. 
Published: September 2008

AbstractThis paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius—Perron operator for such maps. The method is applied to estimate the Lyapunov exponents for a planar map of recent interest.
Formes normales d'équations differéntielles implicites et de champs de Liouville
Authors: Manouchehri M. 
Published: September 2008

AbstractConsider the partial differential equation f(x, y(x), dy(x)) = 0, where f is a smooth real function on ℝn × ℝ × (ℝn)*. Near each singularity of the characteristic foliation, a Liouville field is associated to the equation; we classify hyperbolic germs of Liouville fields up to symplectic transformations, hence we deduce normal forms for partial differential equations up to transformations which preserve the standard contact form of ℝ2n+1. For n = 1, a theorem of Davydov enables us to deduce normal forms for such equations up to transformations of the x, y plane.
Fractal dimensions of almost periodic attractors
Authors: Naito Koichiro 
Published: September 2008

AbstractIn this paper we estimate fractal dimensions of almost periodic orbits in terms of two kinds of exponents: the exponent in the inclusion lengths for ε-almost period and the exponent in Hölder conditions. Further, we estimate the inclusion lengths for ε-almost period of quasi-periodic functions by using Diophantine approximations. In the n-frequency quasi-periodic case we can show that the fractal dimension of its orbit is majorized by the value n/δ when it is Hölder continuous with exponent δ, 0 < δ ≤ 1.
Transitive maps which are not ergodic with respect to Lebesgue measure
Authors: Van Strien Sebastian 
Published: September 2008

AbstractIn this paper we shall give examples of rational maps on the Riemann sphere and also of polynomial interval maps which are transitive but not ergodic with respect to Lebesgue measure. In fact, these maps have two disjoint compact attractors whose attractive basins are ‘intermingled’, each having a positive Lebesgue measure in every open set. In addition, we show that there exists a real bimodal polynomial with Fibonacci dynamics (of the type considered by Branner and Hubbard), whose Julia set is totally disconnected and has positive Lebesgue measure. Finally, we show that there exists a rational map associated to the Newton iteration scheme corresponding to a polynomial whose Julia set has positive Lebesgue measure.
Hausdorff dimension of Julia sets of complex Hénon mappings
Authors: Verjovsky A. , Wu H. 
Published: September 2008

AbstractThe Hausdorff dimension of closed invariant sets under diffeomorphisms is an interesting concept as it is a measure of their complexity. The theory of holomorphic dynamical systems provides us with many examples of fractal sets and, in particular, a theorem of Ruelle [Ru1] shows that the Hausdorff dimension of the Julia set depends real analytically onfiffis a rational function of ℂ and the Julia setJoffis hyperbolic. In this paper we generalize Ruelle's result for complex dimension two and show the real analytic dependence of the Hausdorff dimension of the corresponding Julia sets of hyperbolic Hénon mappings.
Return times and conjugates of an antiperiodic transformation
Authors: Alpern Steve 
Published: September 2008

AbstractDenote by G the group of all μ-preserving bijections of a Lebesgue probability space (X, Σ, μ) and by C the conjugacy class of an antiperiodic transformation σ in G. We present several new results concerning the denseness of C in G with respect to various topologies. One of these asserts that given any weakly mixing transformation τ in G and any F with μ(F) < 1, there is a transformation in C which agrees with τ a.e. on F.
Real-expansive flows and topological dimension
Authors: Keynes H. B. , Sears M. 
Published: September 2008

AbstractWe examine generalizations of R. Mañé's results on the topological dimension of spaces supporting an expansive homeomorphism to the case of real-expansive flows. We show that a space supporting a real-expansive flow must be finite dimensional, and a minimal real-expansive flow not exhibiting a type of spiral behaviour must be one-dimensional. This latter class includes all known examples and a slight generalization of Axiom A flows. These results are obtained by introducing a new concept of stable and unstable sets for real flows, and examining real-expansive flows in terms of these sets.
Self-generation of self-replicating maps of an interval
Authors: Parry William 
Published: September 2008

AbstractWe construct C1 symmetric maps of [−1, 1] to itself, satisfying a condition similar to Feigenbaum's: -φ(x) = φ(-x), φ2(bx) = bφ(x), 0<b <1. Under certain conditions, the non-wandering set consists of the one-sided Morse minimal set together with 2n points of period 2n for each n = 1, 2, … The main significance of the construction is its simplicity. Given a certain piece of the map φ, the rest is generated by the required equation.
Divergence type of some subgroups of finitely generated Fuchsian groups
Authors: Rees Mary 
Published: September 2008

AbstractLet Г be a finitely generated discrete subgroup of the isometries of the hyperbolic plane H2 with at least one parabolic element. We prove that, if Г1 is a subgroup of Г with Г/Г1 abelian, the ‘critical exponent’ of Г1 is the same as that of Г. We give necessary and sufficient conditions-in terms of the rank of Г/Г1, the critical exponent of Г, and the image of parabolic elements of Г in Г/Г1 - for the Poincaré series of Г1 to diverge at the critical exponent.
Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
Authors: Schmidt Klaus 
Published: September 2008

AbstractThis paper discusses the relations between the following properties o finite measure preserving ergodic actions of a countable group G: strong ergodicity (i.e. the non-existence of almost invariant sets), uniqueness of G-invariant means on the measure space carrying the group action, and certain cohomological properties. Using these properties one can characterize all actions of amenable groups and of groups with Kazhdan's property T. For groups which fall in between these two definations these notions lead to some interesting examples.
Orbit equivalence and rigidity of ergodic actions of Lie groups
Authors: Zimmer Robert J. 
Published: September 2008

AbstractThe rigidity theorem for ergodic actions of semi-simple groups and their lattice subgroups provides results concerning orbit equivalence of the actions of these groups with finite invariant measure. The main point of this paper is to extend the rigidity theorem on one hand to actions of general Lie groups with finite invariant measure, and on the other to actions of lattices on homogeneous spaces of the ambient connected group possibly without invariant measure. For example, this enables us to deduce non-orbit equivalence results for the actions of SL (n, ℤ) on projective space, Euclidean space, and general flag and Grassman varieties.
Design rationale: Researching under uncertainty
Authors: Burge Janet E. 
Published: September 2008

AbstractRationale research in software development is a challenging area because although there is no shortage of advocates for its value, there is also no shortage of reasons for why rationale is unlikely to be captured in practice. Despite more than 30 years of research there still remains much uncertainty: how useful are the potential benefits and how insurmountable are the barriers? Will the value of the rationale (design and otherwise) justify the cost of collecting it? Although there have been numerous rationale research projects, many, if not most, received little or no empirical evaluation. There also have not been many studies examining what the needs are of the practitioners who would be supported by the rationale. This article discusses the “doom and gloom” predictions of rationale's failure, provides a survey of evaluations of rationale systems, and discusses what we hope is a brighter outlook for rationale research in the future. There are development standards and synergistic research areas that may help with rationale research and its acceptance in the software community with which we should be working. This article also presents the results of a pilot survey of software developers who were asked how they would envision using rationale and what they believe the most important barriers are. Although some results were as expected, there were also some surprises. Research on technology transfer indicates that, among other things, to transition successfully from research into practice we need to understand the need that is being met and demonstrate the value of our approach. Until we have determined how our work is needed by the people we are trying to help we will remain researching under uncertainty.