bluuebunny/crossref_metadata_2025_split huggingface dataset:
Periodic points and invariant pseudomeasures for toral endomorphisms
Authors: Veech William A. 
Published: September 2008

AbstractExtending a result of Livsic [10] it is proved that the coboundary equation f(Tx)−f(x) = g(x) admits a C∞ solution f for C∞g when T is an ergodic toral endomorphism and g sums to zero over every periodic orbit. The same statement is false with C1 in place of C∞, in contrast to the Livsic (hyperbolic) theorem. In one dimension the ‘Lip α’ case leads to questions relating to the generalized Riemann hypothesis.
Almost inductive limit automorphisms and embeddings into AF-algebras
Authors: Voiculescu Dan 
Published: September 2008

AbstractThe crossed product of an AF-algebra by an automorphism, a power of which is approximately inner, is shown to be embeddable into an AF-algebra. The proof uses almost inductive limit automorphisms, i.e. automorphisms possessing a sequence of almost invariant finite-dimensional C*-subalgebras converging to the given AF-algebra.
Dynamics of entire functions near the essential singularity
Authors: Devaney Robert L. , Tangerman Folkert 
Published: September 2008

AbstractWe show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).
A refinement of the Conley index and an application to the stability of hyperbolic invariant sets
Authors: Floer Andreas 
Published: September 2008

AbstractA compact and isolated invariant set of a continuous flow possesses a so called Conley index, which is the homotopy type of a pointed compact space. For this index a well known continuation property holds true. Our aim is to prove in this context a continuation theorem for the invariant set itself, using an additional structure. This refinement of Conley's index theory will then be used to prove a global and topological continuation-theorem for normally hyperbolic invariant sets.
Periodic orbits for dissipative twist maps
Authors: Casdagli Martin 
Published: September 2008

AbstractWe develop simple topological criteria for the existence of periodic orbits in maps of the annulus. These are applied to one-parameter families of dissipative twist maps of the annulus and their attractors. It follows that many of the motions found by variational methods in area preserving twist maps also occur in the dissipative case.
Loose Bernoullicity is preserved under exponentiation by integrable functions
Authors: Rahe Maurice H. , Rudolph Daniel J. 
Published: September 2008

AbstractIt is known that if Ω is a Lebesgue space, T:Ω→Ω is a loosely Bernoulli transformation, and L is a fixed non-zero integer, then the transformation S = TL will again be loosely Bernoulli on each ergodic component. In this note, the above stated result is extended to include the case where L is an arbitrary integrable integer-valued function on Ω.
Dynamics of Markov chains and stable manifolds for random diffeomorphisms
Authors: Brin M. , Kifer Yu. 
Published: September 2008

AbstractWe consider the Markov chain on a compact manifold M generated by a sequence of random diffeomorphisms, i.e. a sequence of independent Diff2(M)-valued random variables with common distribution. Random diffeomorphisms appear for instance when diffusion processes are considered as solutions of stochastic differential equations. We discuss the global dynamics of Markov chains with continuous transition densities and construct non-random stable foliations for random diffeomorphisms.
A counter-example to a C2 closing lemma
Authors: Gutierrez C. 
Published: September 2008

AbstractLet M be a compact manifold that contains a two-dimensional punctured torus. Given p ∈ M and an integer r ≥ 2, there exists X ∈ ∞(M) having non-trivial recurrent trajectories and such that, for some neighbourhood of X|(M−{p}) in r(M−{p}), no Y ∈ has closed orbits.
On ergodic actions whose self-joinings are graphs
Authors: del Junco A. , Rudolph D. 
Published: September 2008

AbstractWe call an ergodic measure-preserving action of a locally compact group G on a probability space simple if every ergodic joining of it to itself is either product measure or is supported on a graph, and a similar condition holds for multiple self-joinings. This generalizes Rudolph's notion of minimal self-joinings and Veech's property S.Main results The joinings of a simple action with an arbitrary ergodic action can be explicitly descnbed. A weakly mixing group extension of an action with minimal self-joinings is simple. The action of a closed, normal, co-compact subgroup in a weakly-mixing simple action is again simple. Some corollaries. Two simple actions with no common factors are disjoint. The time-one map of a weakly mixing flow with minimal self-joinings is prime Distinct positive times in a -action with minimal self-joinings are disjoint.
Points génériques de Champernowne sur certains systèmes codes; application aux θ-shifts
Authors: Bertrand-Mathis Anne 
Published: September 2008

AbstractWe show that if messages of length one, two, three…of a code X which verifies ρx* < ρx are concatenated, we obtain a point generic for an invariant measure on the dynamical system associated to the code; this measure is induced by the maximal measure on the tower studied by Hansel and Blanchard.Résumé. Nous montrons que si nous alignons les messages de longueur 1, puis 2, et ainsi de suite, d'un code X vérifiant ρx* < ρx, nous obtenons un point générique pour une mesure invariante sur le système dynamique associé au code en question; nous montrons que cette mesure se trouve être la mesure induite par la mesure d'entropie maximale sur la tour associée au code introduite par Hansel et Blanchard. Nous en déduisons des points génériques pour les systèmes sofiques et les θ-shifts munis de leur mesure maximale.
The attracting centre of a continuous self-map of the interval
Authors: Jincheng Xiong 
Published: September 2008

AbstractLet ƒ denote a continuous map of a compact interval I to itself. A point x ∈ I is called a γ-limit point of ƒ if it is both an ω-limit point and an α-limit point of some point y ∈ I. Let Γ denote the set of γ-limit points. In the present paper, we show that (1) −Γ is either empty or countably infinite, where denotes the closure of the set P of periodic points, (2) x ∈ I is a γ-limit point if and only if there exist y1 and y2 in I such that x is an ω-limit point of y1, and y1 is an ω-limit point of y2, and if and only if there exists a sequence y1, y2,…of points in I such that x is an ω-limit point of y1, and yi is an ω-limit point of yi+1 for every i ≥ 1, and (3) the period of each periodic point of ƒ is a power of 2 if and only if every γ-limit point is recurrent.
On the construction of smooth ergodic skew-products
Authors: Nerurkar Mahesh G. 
Published: September 2008

AbstractIn this paper we prove results about lifting dynamical and ergodic properties of a given smooth dynamical system to its skew-product extensions by smooth cocycles. The classical small divisor argument shows that in general such results are not possible. However, using the notion of the ‘fast periodic approximation’ introduced by A. Katok, we will show that if the dynamical system admits such a ‘fast periodic approximation’ then indeed a certain qualitative behaviour which is prohibited by small divisor type conditions is now in fact generic. The techniques are also applied to show that ‘recurrent-proximal’ behaviour of solutions of linear differential equations with almost periodic coefficients is generic under suitable conditions on the coefficient matrix.
Joint ergodicity for group actions
Authors: Bergelson Vitaly , Rosenblatt Joseph 
Published: September 2008

AbstractLet T1,…,Tn be continuous representations of a σ-compact separable locally compact amenable group G as measure-preserving transformations of a non-atomic separable probability space (X, β, m). Let (Kn) be a right Følner sequence of compact sets in G. If T1,…,Tn are pairwise commuting in the sense that Ti(g)Tj(h) = Tj(h)Ti(g) for i ≠ j and g, h ∈ G, then necessary and sufficient conditions can be given, in terms of the ergodicity of certain tensor products, for the following to hold: for all F1,…,Fn∈L∞, the sequence AN(x) whereconverges in L2(X) to . The necessary and sufficient conditions are that each of the following representations are ergodic: Tn, Tn−1⊗Tn−1Tn,…,T2⊗T2T3⊗…⊗T2…Tn, T1⊗T1T2⊗…⊗T1…Tn.In order to prove this theorem, specific properties of the decomposition of L2(X) into its weakly mixing and compact subspaces with respect to a representation Ti are needed. These properties are also used to prove some generalizations of wellknown facts from ergodic theory in the case where G is the integer group Z.
Automorphisms of solenoids and p-adic entropy
Authors: Lind D. A. , Ward T. 
Published: September 2008

AbstractWe show that a full solenoid is locally the product of a euclidean component and p-adic components for each rational prime p. An automorphism of a solenoid preserves these components, and its topological entropy is shown to be the sum of the euclidean and p-adic contributions. The p-adic entropy of the corresponding rational matrix is computed using its p-adic eigenvalues, and this is used to recover Yuzvinskii's calculation of entropy for solenoidal automorphisms. The proofs apply Bowen's investigation of entropy for uniformly continuous transformations to linear maps over the adele ring of the rationals.
A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity
Authors: Nowicki Tomasz 
Published: September 2008

AbstractA positive Liapunov exponent for the critical value of an S-unimodal mapping implies a positive Liapunov exponent of the backward orbit of the critical point, uniform hyperbolic structure on the set of periodic points and an exponential diminution of the length of the intervals of monotonicity. This is the proof of the Collet-Eckmann conjecture from 1981 in the general case.
Entropy and semi-conjugacy in dimension two
Authors: Handel Michael 
Published: September 2008

AbstractWe prove that if a diffeomorphism f of a closed surface is homotopic to and has the same topological entropy as a pseudo-Anosov homeomorphism g, then f is semi-conjugate to g. As part of the proof, a necessary and sufficient condition is given for a pseudo-orbit of a pseudo-Anosov homeomorphism g to be shadowed by an actual orbit of g.
Mixing and asymptotic distribution modulo 1
Authors: Lyons Russell 
Published: September 2008

AbstractIf μ is a probability measure which is invariant and ergodic with respect to the transformationx↦qxon the circle ℝ/ℤ, then according to the ergodic theorem, {qnx} has the asymptotic distribution μ for μ-a.e.x. On the other hand, Weyl showed that when μ is Lebesgue measure, λ, and {mj} is an arbitrary sequence of integers increasing strictly to ∞, the asymptotic distribution of {mjx} is λ for λ-a.e.x. Here, we investigate the asymptotic distributions of {mjx} μ-a.e. for fairly arbitrary {mj} under some strong mixing conditions on μ. The result is a kind of stable ergodicity: the distributions are obtained from simple operations applied to μ. The ideas extend to the situation of a sequence of transformationsx↦qnxwhere invariance is not present. This gives us information about many Riesz products and Bernoulli convolutions. Finally, we apply the theory to resolve some questions aboutH-sets.
Ω-Stability is not dense in Axiom A
Authors: Patterson S. E. 
Published: September 2008

AbstractAn example of a diffeomorphism f on a three dimensional manifold M3 is constructed so that f satisfies Axiom A, has a cycle and f has a neighborhood N in Diffr (M3) so that each g in N is not Ω-stable. Existing techniques allow one to extend this example to any compact manifold of dimension greater than two.
Existence de cycles pour des multi-applications du cercle
Authors: Dufour Jean-Paul 
Published: September 2008

AbstractWe consider multi-applications Γ of the circleS1, the graphs of which are ‘degree (1, 1)’, continuous piece-wise monotonic curves ofS1×S1In general Γpis not a connected curve but it is a union of a degree (1, 1) continuous curve ΓpofS1×S1and of some other curves homotopic to a point. Using these Γpwe are able to study dynamics of Γ. We focus on the case where Γ has no periodic points and we see, for instance, that all ‘regular’ orbits have, onS1the same order as orbits of an irrational rotation. Using this we prove that such F without ‘cycles’ are obtained from a Denjoy's counter-example, perturbing it in the holes of the invariant set. Finally we generalize the classical result of Block and Franke showing that if Γ is aC2curve with no degenerate critical points, or if Γ is aC∞ curve with no ‘flat’ points, there are always ‘cycles’, unless Γ is an homeomorphism.
Singularities of vector fields on ℝ3 determined by their first non-vanishing jet
Authors: Bonckaert Patrick , Dumortier Freddy , Strien Sebastian Van 
Published: September 2008

AbstractIn this paper we will present a result which gives a sufficient condition for a vector field X on ℝ3 to be equivalent at a singularity to the first non-vanishing jet jkX(p) of X at p. This condition - which only depends on the homogeneous vector field defined by jkX(p) - is stated in terms of the blown-up vector field (which is defined on S2xℝ), and essentially means that there are no saddleconnections for |S2×{0}.The key tool in the proof will be a result of local normal linearization along a codimension 1 submanifold M providing a C0 conjugacy having a normal derivative along M equal to 1.
Rigidity in topological dynamics
Authors: Glasner S. , Maon D. 
Published: September 2008

AbstractBy analogy with the ergodic theoretical notion, we introduce notions of rigidity for a minimal flow (X, T) according to the various ways a sequence Tni can tend to the identity transformation. The main results obtained are:(i) On a rigid flow there exists a T-invariant, symmetric, closed relation Ñ such that (X, T) is uniformly rigid iff Ñ = Δ, the diagonal relation.(ii) For syndetically distal (hence distal) flows rigidity is equivalent to uniform rigidity.(iii) We construct a family of rigid flows which includes Körner's example, in which Ñ exhibits various kinds of behaviour, e.g. Ñ need not be an equivalence relation.(iv) The structure of flows in the above mentioned family is investigated. It is shown that these flows are almost automorphic.
Equivariant spectral decomposition for flows with a ℤ-action
Authors: Mosher Lee 
Published: September 2008

AbstractGiven a manifold equipped with a free, properly discontinuous, cocompact ℤ-action, and a flow on which is ℤ-equivariant, we study the qualitative dynamics of . Under certain hypotheses on , we show that the chain recurrent set of has a decomposition which is the analogue, in the category of ℤ-equivariant flows, of Smale's spectral decomposition for recurrent sets of Axiom A flows.
Homomorphismes entre systèmes dynamiques définis par substitutions
Authors: Host B. , Parreau F. 
Published: September 2008

AbstractOn étudie ici les homomorphismes métriques entre systèmes dynamiques definis par des substitutions de même longueur. En général, ces homomorphismes sont continus, et ont une forme simple. Le commutant essentiel d'un système dynamique defini par une substitution est fini, et peut être déterminé explicitement.
An algorithm for calculating critical probabilities and percolation functions in percolation models defined by rotations
Authors: Meester Ronald W. J. 
Published: September 2008

AbstractA class of percolation models on ℤd is developed in which the stochastic structure is provided by means of a d-parameter dynamical system. Of particular interest are those models generated by circle rotations. Unlike for independent models, the critical value and the percolation function can be explicitly calculated. These calculations lead to a conjecture concerning the behaviour of a related dynamical system.
Subsystems, Perron numbers, and continuous homomorphisms of Bernoulli shifts
Authors: Tuncel Selim 
Published: September 2008

AbstractLet S, T be subshifts of finite type, with Markov measures p, q on them, and let φ: (S, p) → (T, q) be a block code. Let Ip, Iq denote the information cocycles of p, q. For a subshift of finite type ⊂T, the pressure of equals that of . Applying this to Bernoulli shifts and using finiteness conditions on Perron numbers, we have the following. If the probability vector p = (p1…, pk+1) is such that the distinct transcendental elements of {p1/pk+1…pk/pk+1) are algebraically independent then the Bernoulli shift B(p) has finitely many Bernoulli images by block codes.
Non-smooth geodesic flows and the earthquake flow on Teichmüller space
Authors: Weiss Howard 
Published: September 2008

AbstractThurston generalized the notion of a twist deformation about a simple closed geodesic on a hyperbolic Riemann surface to a twisting or shearing along a much more complicated object called a measure geodesic lamination. This new deformation is called an earthquake and it generates a flow on the tangent bundle of Teichmüller space.In this paper we study the earthquake flow. We show that the flow is not smooth and that it is not the geodesic flow for an affine connection. We also derive the explicit form of the system of differential equations which earthquake trajectories satisfy.
The geometry of measured geodesic laminations and measured train tracks
Authors: Weiss Howard 
Published: September 2008

AbstractThurston and Kerckhoff have shown that the space of measured geodesic laminations on a hyperbolic Riemann surface serves as a non-linear model of the tangent space to Teichmüller space at the surface. In this paper we show that the natural map between these manifolds has stronger than Hölder continuous regularity.
The differentiability of the conjugation of certain diffeomorphisms of the circle
Authors: Katznelson Y. , Ornstein D. 
Published: September 2008

AbstractOur purpose in this paper is to present a more or less complete solution to the problem of the smoothness of the conjugation of aperiodic diffeomorphisms of the circle. We show that the rotation number and the smoothness of the diffeomorphism guarantee a certain smoothness for the homeomorphism which conjugates it with a rigid rotation, and obtain the best smoothness that can be guaranteed.
On the almost everywhere convergence of the ergodic averages
Authors: Martín-Reyes F. J. , De La Torre A. 
Published: September 2008

AbstractLet (X, ν) be a finite measure space and let T: X → X be a measurable transformation. In this paper we prove that the averages converge a.e. for every f in Lp(dν), 1 < p < ∞, if and only if there exists a measure γ equivalent to ν such that the averages apply uniformly Lp(dν) into weak-Lp(dγ). As a corollary, we get that uniform boundedness of the averages in Lp(dν) implies a.e. convergence of the averages (a result recently obtained by Assani). In order to do this, we first study measures v equivalent to a finite invariant measure μ, and we prove that supn≥0An(dν/dμ)−1/(p−1) a.e. is a necessary and sufficient condition for the averages to converge a.e. for every f in Lp(dν).
An explosion point for the set of endpoints of the Julia set of λ exp (z)
Authors: Mayer John C. 
Published: September 2008

AbstractThe Julia set Jλ of the complex exponential function Eλ: z → λez for a real parameter λ(0 < λ < 1/e) is known to be a Cantor bouquet of rays extending from the set Aλ of endpoints of Jλ to ∞. Since Aλ contains all the repelling periodic points of Eλ, it follows that Jλ = Cl (Aλ). We show that Aλ is a totally disconnected subspace of the complex plane ℂ, but if the point at ∞ is added, then is a connected subspace of the Riemann sphere . As a corollary, Aλ has topological dimension 1. Thus, ∞ is an explosion point in the topological sense for Âλ. It is remarkable that a space with an explosion point occurs ‘naturally’ in this way.
The splitting of separatrices for analytic diffeomorphisms
Authors: Fontich E. , Simó C. 
Published: September 2008

AbstractWe study families of diffeomorphisms close to the identity, which tend to it when the parameter goes to zero, and having homoclinic points. We consider the analytical case and we find that the maximum separation between the invariant manifolds, in a given region, is exponentially small with respect to the parameter. The exponent is related to the complex singularities of a flow which is taken as an unperturbed problem. Finally several examples are given.
Meromorphic extension of the zeta function for Axiom A flows
Authors: Haydn Nicolai T. A. 
Published: September 2008

AbstractWe prove the meromorphicity of the zeta function on shifts of finite type for Hölder continuous functions assuming that the essential spectrum of the associated Ruelle operator is contained in the open unit disc. This result allows to extend the region of meromorphicity of the zeta function for Axiom A flows by a strip whose width is determined by the contraction rate of the flow.
Minimal convergence on Lp spaces
Authors: Assani I. 
Published: September 2008

AbstractLet (X, F, μ) be a probability measure space, p and β real numbers such that 1≤p<+∞ and 0<β<p. For any linear positive operator T satisfying T1, T*1 = 1 we prove the norm and pointwise convergence of the sequence We get then the pointwise and norm convergence in Lp, 0 < β ≥ 1 < p < 2, of the sequence sgn Sif for any positive linear operator on Lp(Ω, A, μ) (μ-σ-finite) verifying ∥(1 − α)I + αS∥p ≤ 1 for a real number 0 < α < 1. In the particular case α = 1, (S is a contraction), β = p−l, this result gives the pointwise and norm convergence of the sequences introduced by Beauzamy and Enflo in 1985 to the asymptotic center of the sequence .
Automorphisms of one-sided subshifts of finite type
Authors: Boyle Mike , Franks John , Kitchens Bruce 
Published: September 2008

AbstractWe prove that the automorphism group of a one-sided subshift of finite type is generated by elements of finite order. For one-sided full shifts we characterize the finite subgroups of the automorphism group. For one-sided subshifts of finite type we show that there are strong restrictions on the finite subgroups of the automorphism group.
Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire
Authors: Guivarc'h Yves 
Published: September 2008

AbstractUsing the asymptotic properties of products of random matrices we study some properties of the subgroups of the linear group. These properties are centered around the theorem of J. Tits giving the existence of free subgroups in linear groups.
The box and Hausdorff dimension of self-affine sets
Authors: Bedford Tim , Urbański Mariusz 
Published: September 2008

AbstractUnder a natural assumption the Hausdorff dimension of a measure μ canonically associated with a given self-affine set is computed. A simplified proof of Bowen's formula for the box dimension of self-affine sets proved earlier is given. A condition for the box dimension and Hausdorff dimension to be equal is proven, and a collection of examples in which this condition can be checked is discussed.
Bernoulli shifts of the same entropy are finitarily and unilaterally isomorphic
Authors: Del Junco Andrés 
Published: September 2008

AbstractLetp= {p1,  ,pn} andq= {qi,  ,qm} be finite probability vectors, each having at least three non-zero components, such that. LetC= {1,  ,n},D= {1,  ,m} and let (Cℤ,pℤ, σ) and (Dℤ,qℤ, σ) be the corresponding Bernoulli shifts. Then there exists an isomorphism φ between these shifts such that for a.a.x∈ Cℤσ(x)(0) is determined by finitely many of the future co-ordinatesx(0),x(1),   and for a. a.y∈Dℤφ−1(y)(0) is determined by finitely many of the co-ordinates  y(−1),y(0),y(1),  .