bluuebunny/crossref_metadata_2025_split huggingface dataset:
Exponents, attractors and Hopf decompositions for interval maps
Authors: Keller Gerhard 
Published: September 2008

AbstractOur main results, specialized to unimodal interval maps T with negative Schwarzian derivative, are the following:(1) There is a set CT such that the ω-limit of Lebesgue-a.e. point equals CT. CT is a finite union of closed intervals or it coincides with the closure of the critical orbit.(2) There is a constant λT such that for Lebesgue-a.e. x.(3) λT > 0 if and only if T has an absolutely continuous invariant measure of positive entropy.(4) , i.e. uniform hyperbolicity on periodic points implies λT > 0, and λT < 0 implies the existence of a stable periodic orbit.
An area approach to wandering domains for smooth surface endomorphisms
Authors: Norton Alec 
Published: September 2008

AbstractWe prove an infinite-area lemma for maps which are area non-contracting on the boundaries of certain domains; the maps are required to be smooth to the extent that their Jacobians are twice differentiable (see Main Lemma below). It will follow that a hyperbolic rational map has no wandering simply connected domains. As a more direct corollary, a C3 diffeomorphism f of a compact smooth 2-manifold cannot have a wandering domain Δ if f is area non-contracting on the boundary of each forward image of Δ.
Analysis of a procedure for finding numerical trajectories close to chaotic saddle hyperbolic sets
Authors: Nusse Helena E. , Yorke James A. 
Published: September 2008

AbstractIn dynamical systems examples are common in which there are regions containing chaotic sets that are not attractors, e.g. systems with horseshoes have such regions. In such dynamical systems one will observe chaotic transients. An important problem is the ‘Dynamical Restraint Problem’: given a region that contains a chaotic set but contains no attractor, find a chaotic trajectory numerically that remains in the region for an arbitrarily long period of time.We present two procedures (‘PIM triple procedures’) for finding trajectories which stay extremely close to such chaotic sets for arbitrarily long periods of time.
Local product structure for group actions
Authors: Ramsay Arlan 
Published: September 2008

AbstractA differentiable G-space is introduced, for a Lie group G, into which every countably separated Borel G-space can be imbedded. The imbedding can be a continuous map if the space is a separable metric space. Such a G-space is called a universal G-space. This universal G-space has a local product structure for the action of G. That structure is inherited by invariant subspaces, giving a local product structure on general G-spaces. This information is used to prove that G-spaces are stratified by the subsets consisting of points whose orbits have the same dimension, to prove that G-spaces with stabilizers of constant dimension are foliated, to give a short proof that closed subgroups of Lie groups are Lie groups, to give a new proof and a stronger version of the Ambrose—Kakutani Theorem and to give a new proof of the existence of near-slices at points having compact stabilizers and hence of the existence of slices for Cartan G-spaces.
Invariant curves and time-dependent potentials
Authors: Laederich Stephane , Lev Mark 
Published: September 2008

AbstractIn this paper we prove the existence of invariant curves and thus stability for all time for a class of Hamiltonian systems with time-dependent potentials, namely, for systems of the formwhereis a superquadratic polynomial potential with periodic coefficients. As a limiting case, a proof of the stability of Ulam's problem of a particle bouncing between two periodicially moving walls is given.
Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques
Authors: Lesigne Emmanuel 
Published: September 2008

AbstractWe call nilmanifold every compact space X on which a connected locally compact nilpotent group acts transitively. We show that, if X is a nilmanifold and f is a continuous function on X, then, for all x in X and a in N, the sequenceconverges. We give a process for the computation of the limit. A similar result for the continuous means is presented.
The action of inert finite-order automorphisms on finite subsystems of the shift
Authors: Boyle Mike , Fiebig Ulf-Rainer 
Published: September 2008

AbstractLet (X, S) be a shift of finite type. Let G be the group of automorphisms of (X, S) which are compositions of elements of finite order in the kernel of the dimension representation. We characterize the action of G on finite subsystems of (X, S).
Exceptional minimal sets of C1+α-group actions on the circle
Authors: Hurder S. 
Published: September 2008

AbstractWe prove two extensions of Sacksteder's Theorem for the action A: Γ × S1 → S1 of a finitely-generated group Γ on the circle by C1+α-diffeomorphisms. If the action A has an exceptional minimal set K with a gap endpoint of exponential orbit growth rate, or if the action A on K has positive topological entropy, then the exceptional set K is hyperbolic. That is, A has a linearly contracting fixed-point in K. A key point of the paper is to prove a foliation closing lemma using the foliation geodesic flow technique.
Smooth Markov partitions and toral automorphisms
Authors: Cawley Elise 
Published: September 2008

AbstractWe show that the only hyperbolic toral automorphisms f for which there exist Markov partitions with piecewise smooth boundary are those for which a power fk is linearly covered by a direct product of automorphisms of the 2-torus. Only a finite number of shapes occur in a certain natural set of cross-sections of the partition boundary. The behavior of the stratified structure of a piecewise smooth boundary under the mapping forces these shapes to be self-similar. This, together with expanding properties of the mapping, means that a piecewise smooth partition is in fact piecewise linear. Orbits of affine disks in the boundary are used to construct a basis of 2-dimensional invariant toral subgroups, and then the product decomposition of a covering follows easily.
Random iterations of rational functions
Authors: Fornaess John Erik , Sibony Nessim 
Published: September 2008

AbstractWe study the asymptotic behavior of iterates of rational functions with small perturbations. In presence of attractive cycles we show that almost surely, in the parameter space, the iterates converge to a given neighborhood of the attractive cycles. When there is no attractive cycle, we prove an ergodic theorem with respect to Lebesgue measure.
Groups acting freely on R-trees
Authors: Morgan John W. , Skora Richard K. 
Published: September 2008

AbstractIn this paper we study the question of which groups act freely on R-trees. The paper has two parts. The first part concerns groups which contain a non-cyclic, abelian subgroup. The following is the main result in this case.Let the finitely presented group G act freely on an R-tree. If A is a non-cyclic, abelian subgroup of G, then A is contained in an abelian subgroup A′ which is a free factor of G.The second part of the paper concerns groups whch split as an HNN-extension along an infinite cyclic group. Here is one formulation of our main result in that case.Let the finitely presented group G act freely on an R-tree. If G has an HNN-decompositionwhere (s) is infinite cyclic, then there is a subgroup H′ ⊂ H such that either(a); or(b),where S is a closed surface of non-positive Euler characteristic.A slightly different, more precise result is also given.
Integral formulas for the Laplacian along the unstable foliation and applications to rigidity problems for manifolds of negative curvature
Authors: Yue Chengbo 
Published: September 2008

AbstractWe obtain a class of integral formulas for the Lapacian along unstable leaves of the geodesic flow of compact manifolds of negative curvature. Using these formulas, we give two functional descriptions of those manifolds with horospheres having constant mean curvature. More rigidity problems are discussed, including a simple proof of two important Lemmas by Hamenstadt which avoids her use of stochastic process.
The return times and the Wiener—Wintner property for mean-bounded positive operators in Lp
Authors: Assani I. 
Published: September 2008

AbstractWe prove the following two results for mean-bounded positive operators on Lp(µ) (1<p>∞).(1) If (X, , µ, ϕ) is a dynamical system and f ∈ L∞ (X) then the sequence f(ϕn x) is a.e. a universal good sequence for mean-bounded positive operators in Lp. (Return times property.)(2) If T is a mean-bounded positive operator on LP(X, , µ) and f ∈ Lp (µ) then the sequence Tnf)(x) is a.e. a universal good sequence for all dynamical systems (Y, , v,S) in L∞(v). A corollary of (2) is a Wiener-Wintner property for mean-bounded positive operators on Lp.
Geometric measures for parabolic rational maps
Authors: Denker M. , Urbański M. 
Published: September 2008

AbstractLet h denote the Hausdorff dimension of the Julia set J(T) of a parabolic rational map T. In this paper we prove that (after normalisation) the h-conformal measure on J(T) equals the h-dimensional Hausdorff measure Hh on J(T), if h ≥ 1, and equals the h-dimensional packing measure Πh on J(T), if h ≤ 1. Moreover, if h < 1, then Hh = 0 and, if h > 1, then Πh(J(T)) = ∞.
Time-preserving conjugacies of geodesic flows
Authors: Hamenstädt Ursula 
Published: September 2008

AbstractIn this note we study Borel-probability measures on the unit tangent bundle ofa compact negatively curved manifold M that are invariant under the geodesic flow. We interpret the entropy of such a measure as a Hausdorff dimension with respect to a natural family of distances on the ideal boundary of the universal covering of M. This in term yields necessary and sufficient conditions for the existence of time preserving conjugacies of geodesic flows.
There are no minimal homeomorphisms of the multipunctured plane
Authors: Handel Michael 
Published: September 2008

The main results of this paper are the following theorem and its corollary.Theorem 0.1. Suppose that f: S2 → S2 is an orientation-preserving homeomorphism of the two-dimensional sphere and that Fix (f) is a finite set containing at least three points. If f has a dense orbit then the number of periodic points of period n for some iterate of f grows exponentially in n.
Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties
Authors: Pesin Ya. B. 
Published: September 2008

AbstractWe introduce a class of dynamical systems on a Riemannian manifold with singularities having attractors with strong hyperbolic behavior of trajectories. This class includes a number of famous examples such as the Lorenz type attractor, the Lozi attractor and some others which have been of great interest in recent years. We prove the existence of a special invariant measure which is an analog of the Bowen-Ruelle-Sinai measure for classical hyperbolic attractors and study the ergodic properties of the system with respect to this measure. We also describe some topological properties of the system on the attractor. Our results can be considered a dissipative version of the theory of systems with singularities preserving the smooth measure.
Lyapunov maps, simplicial complexes and the Stone functor
Authors: Robbin Joel W. , Salamon Dietmar A. 
Published: September 2008

AbstractLet be an attractor network for a dynamical system ft: M → M, indexed by the lower sets of a partially ordered set P. Our main theorem asserts the existence of a Lyapunov map ψ:M → K(P) which defines the attractor network. This result is used to prove the existence of connection matrices for discrete-time dynamical systems.
A new proof of the Brouwer plane translation theorem
Authors: Franks John 
Published: September 2008

AbstractLet f be an orientation-preserving homeomorphism of ℝ2 which is fixed point free. The Brouwer ‘plane translation theorem’ asserts that every x0 ∈ ℝ2 is contained in a domain of translation for f i.e. an open connected subset of ℝ2 whose boundary is L ∪ f(L) where L is the image of a proper embedding of ℝ in ℝ2, such that L separates f(L) and f−1(L). In addition to a short new proof of this result we show that there exists a smooth Morse function g: ℝ2 → ℝ such that g(f(x)) < g(x) for all x and the level set of g containing x0 is connected and non-compact (and hence the image of a properly embedded line).
When is an Anosov flow geodesic?
Authors: Green Leon W. 
Published: September 2008

AbstractLet X, H+, H− be vector fields tangent, respectively, to an Anosov flow and its expanding and contracting foliations in a compact three-dimensional manifold, with γ, α+, α− one forms dual to them. If α+([H+, H−]) = α−([H+, H−]) and γ([H+, H−]) = α−([X, H−]) − α+([X, H+]), then the manifold has the structure of the unit tangent bundle of a Riemannian orbifold with geodesic flow field X.
Transfer operators for coupled map lattices
Authors: Keller Gerhard , Künzle Martin 
Published: September 2008

AbstractLet L denote a finite or infinite one-dimensional lattice. To each lattice site is attached a copy of a dynamical system with phase space [0, 1] and dynamics described by a transformation τ: [0, 1] → [0, 1], which is the same on each component. Denote the direct product of these identical systems by T: X → X where X = [0, 1]L. From this product system we obtain a coupled map lattice (CML) Sε: X → X, if we introduce some interaction between the components, e.g. by averaging between nearest neighbours. The strength of the coupling depends upon some parameter ε.For a broad class of piecewise expanding single-component-transformations τ we study such systems via their transfer operators and treat the coupled system as a perturbation of the uncoupled one. This yields existence and stability results for T-invariant measures with absolutely continuous finite-dimensional marginals.
Pascal's triangle, dynamical systems and attractors
Authors: Haeseler Fritz V. , Peitgen Heinz-Otto , Skordev Gencho 
Published: September 2008

AbstractThis paper establishes a global dynamical systems approach for the fractal patterns which are obtained when analysing the divisibility of binomial coefficients modulo a prime power. The general framework is within the class of hierarchical iterated function systems. As a consequence we obtain a complete deciphering of the hierarchical self-similarity features.
The Wiener—Wintner property for the helical transform of the shift on [0, 1]ℤ
Authors: Assani I. 
Published: September 2008

AbstractLet ([0, 1]z, ℬ([0, 1]Z), μz, ϕ) be the dynamical system where ϕ is the shift on the product of the unit interval with Lebesgue measure. We show that this dynamical system has the following properties: (1) there exists ƒ ∈ L1(μz) (in fact in L(Log Log L)β) where 0 <β< 1 for which the following Wiener-Wintner property does not hold: (W-W). There exists a single null set N ⊂ X off which for all x ∈ X/N the sequence converges for all ε ⊂ [0,1).(2) The property (W-W) holds in all Lp(μz), 1< p≤∞. Added to a continuity property of the helical transform, (W-W) is equivalent to the Carleson-Hunt result on the pointwise convergence of Fourier series.
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan
Authors: Bonatti Christian , Kolev Boris 
Published: September 2008

AbstractLet ƒ be an orientation-preserving homeomorphism of the plane such that ƒ-Id is contracting. Under these hypotheses, we establish the existence for every periodic orbit , of a fixed point which has a nonzero linking number with .
Rokhlin towers and closing for flows on T2
Authors: Carroll C. R. 
Published: September 2008

AbstractThis paper considers theclosing problem,r≥2, for flows on T2with finitely many singularities. We study the action of such flows on circles transverse to the flow, using Katznelson and Ornstein's picture of rigid rotations as Rokhlin towers. We are able to obtain closing on purely topological grounds for a large class of flows by means of perturbations which simply twist a flow along an embedded transverse circle (twist-perturbations). However, we give an example of a flow (with finitely many singularities) for which nosmall twist-perturbation yields closing; indeed such perturbations either leave the non-wandering set unchanged or else collapse it to the set of singularities.
Commuting endomorphisms of the circle
Authors: Johnson Aimee S. A. , Rudolph Daniel J. 
Published: September 2008

AbstractIn this paper the results of Shub and Sacksteder are extended to the following theorem: let ƒ1 and ƒ2 be two commuting, expansive, orientation-preserving maps of the circle with a common fixed point and with both in C1+ε or Cr, r ≥2. Assume ƒ1 is p-to-1 and ƒ2 is q-to-1 where p and q generate a nonlacunary semigroup. Then there exists a diffeomorphism g of the same class such that gƒ1g−1 = TP and gƒ2g−1 = Tq.
On dynamics of triangular maps of the square
Authors: Kolyada S. F. 
Published: September 2008

AbstractThe paper is devoted to the triangular maps of the square into itself. The results presented were recently obtained by the author and are briefly stated (in Russian) in a difficult paper as well as those (jointly published with A. N. Sharkovsky) published in ECIT-89 (abstract). All these results are systematized and extended by the new ones. The more detailed proofs of all statements are given. It is shown, for example, that triangular maps exist such that their minimal attraction centres do not coincide with the centres, as well as such ones exist that the Milnor attractor is not contained in the closure of the set of periodic points.
Coalescence of circle extensions of measure-preserving transformations
Authors: Lemańczyk Mariusz , Liardet Pierre , Thouvenot Jean-Paul 
Published: September 2008

AbstractWe prove that for each ergodic automorphism T:(X, ℬ, μ)→(X, ℬ, μ) for which we can find an element S∈C(T) such that the corresponding Z2-action (S, T) on (X, ℬ, μ) is free, there exists a circle valued cocycle φ such that the group extension Tφ is ergodic but is not coalescent. In particular, the existence of such a cocycle is proved for all ergodic rigid automorphisms. As a corollary, in the class of ergodic transformations of [0,1) × [0,1) given byfor each irrational α we find φ such that Tφ is not coalescent. In some special cases the group law of the centralizer is given.
Characterizations of topological dynamical systems whose transformation group C*-algebras are antiliminal and of type 1
Authors: Aoki Nobuo , Tomiyama Jun 
Published: September 2008

AbstractFor a topological dynamical system Σ = (X, σ) where X is a compact metric space with a single homeomorphism σ, we determine the largest postliminal ideal of the transformation group C*-algebra A(Σ) as the intersection of all kernels of irreducible representations of A(Σ) induced from those recurrent points which are not periodic. The result implies characterizations of topological dynamical systems whose transformation group C*-algebras are anti-liminal and post-liminal, that is, of type 1.
Sinai–Ruelle–Bowen measures for N-dimensional derived from Anosov diffeomorphisms
Authors: Carvalho Maria 
Published: September 2008

AbstractThis paper is about the existence of transitive non-hyperbolic attractors with corresponding SRB measures for arcs of diffeomorphisms crossing the boundary of the Axiom A systems, obtained through an elementary generic bifurcation (Hopf, saddle-node or flip) on a transitive Anosov diffeomorphism or an attracting basic set.
Integer Cantor sets and an order-two ergodic theorem
Authors: Fisher Albert M. 
Published: September 2008

AbstractLet denote the orbit closure, under the left shift σ, of the sequence… (all zeroes)… 101000101000000000101 … corresponding to the integer Cantor set . We prove that with respect to the infinite invariant measure ρ, which is the unique normalized non-atomic invariant measure on M, for every f ∈ L1(M, ρ), for ρ-a.e. x∈ Mwhere d = log 2/log 3, and c is the almost-sure value of the right-hand order-two density of the middle-third Cantor set. The proof uses renormalization to a scaling flow, plus identification of (M, σ) as a tower over the Kakutani-von Neumann dyadic odometer.
Some ergodic properties of commuting diffeomorphisms
Authors: Hu Huyi 
Published: September 2008

AbstractFor a smooth ℤ2-action on a C∞ compact Riemannian manifold M, we discuss its ergodic properties which include the decomposition of the tangent space of M into subspaces related to Lyapunov exponents, the existence of Lyapunov charts, and the subadditivity of entropies.
An estimate of entropy for toroidal chaos
Authors: Kwapisz Jaroslaw 
Published: September 2008

AbstractFor a mapping F:ℝ2→ℝ2 being a lift of an isotopic to the identity homeomorphism of the two-dimensional torus the rotation set ρ(F) consists of limit points of all sequences where xi, ∈ ℝ2 and ni→∞. It is known that if ρ(F) has nonempty interior then h(f) (the topological entropy of ƒ) is positive. We provide an estimate from below of h(f) in terms of ρ(F).
Newton's method and a class of meromorphic functions without wandering domains
Authors: Bergweiler Walter 
Published: September 2008

AbstractLetNbe the class of meromorphic functionsfwith the following properties:fhas finitely many poles;f′ has finitely many multiple zeros; the superattracting fixed points offare zeros off′ and vice versa, with finitely many exceptions;fhas finite order. It is proved that iff∈N, thenfdoes not have wandering domains. Moreover, iff∈Nand if ∞ is among the limit functions offnin a cycle of periodic domains, then this cycle contains a singularity off−1. (Herefndenotes thenth iterate off) These results are applied to study Newton's method for entire functionsgof the formwherepandqare polynomials and wherecis a constant. In this case, the Newton iteration functionf(z) =z−g(z)/g′(z) is inN. It follows thatfn(z) converges to zeros ofgfor allzin the Fatou set off, if this is the case for all zeroszofg″. Some of the results can be extended to the relaxed Newton method.
Lefschetz formulae for Anosov flows on 3-manifolds
Authors: Sánchez-Morgado Héctor 
Published: September 2008

AbstractFried has related closed orbits of the geodesic flow of a surface S of constant negative curvature to the R-torsion for a unitary representation of the fundamental group of the unit tangent bundle T1S. In this paper we extend those results to transitive Anosov flows and 2-dimensional attractors on 3-manifolds.
Symplectic displacement energy for Lagrangian submanifolds
Authors: Polterovich Leonid 
Published: September 2008

AbstractRecently H. Hofer defined a new symplectic invariant which has a beautiful dynamical meaning. In the present paper we study this invariant for Lagrangian submanifolds of symplectic manifolds. Our approach is based on Gromov's theory of pseudo-holomorphic curves.
The crossed product of a UHF algebra by a shift
Authors: Bratteli Ola , Størmer Erling , Kishimoto Akitaka , Rørdam Mikael 
Published: September 2008

AbstractWe prove that the crossed product of the CAR algebra M2∞ by the shift is an inductive limit of homogeneous algebras over the circle with fibres full matrix algebras. As a consequence the crossed product has real rank zero, and where is the Cuntz algebra of order 2.
Knaster-like continua and complex dynamics
Authors: Devaney Robert L. 
Published: September 2008

AbstractIn this paper we discuss the topology and dynamics ofEλ(z) = λezwhen λ is real and λ > 1/e. It is known that the Julia set ofEλis the entire plane in this case. Our goal is to show that there are certain natural invariant subsets forEλwhich are topologically Knaster-like continua. Moreover, the dynamical behavior on these invariant sets is quite tame. We show that the only trivial kinds of α- and ω-limit sets are possible.