bluuebunny/crossref_metadata_2025_split huggingface dataset:
Differentiability with respect to parameters of average values in probabilistic contracting dynamical systems
Authors: Withers W. Douglas 
Published: September 2008

AbstractWe consider a dynamical system consisting of a compact subset of RN or CN with several contracting maps chosen with prescribed probabilities, which may depend on position. We show that if the maps and the probabilities are Cl+α functions of the spatial variable and an external parameter, then the average value of a Cl+α function is a differentiate function of the parameter. One implication of this theorem is that for certain families of complex functions dependent on a parameter the reciprocal of the dimension of an invariant measure on the Julia set is a harmonic function of the parameter.
Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere factors also
Authors: Ashley Jonathan 
Published: September 2008

AbstractWe show that if π: ΣG → ΣH is a bounded-to-1 factor map from an irreducible shift of finite type ΣG with period pG to a shift of finite type ΣH with period pH, then there is a factor map that is (pG/pH)-to-1 almost everywhere. Moreover, if π is right closing, then may be taken to be right closing also.
Anosov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature
Authors: Feres Renato , Katok Anatole 
Published: September 2008

AbstractWe consider Anosov flows on a 5-dimensional smooth manifold V that possesses an invariant symplectic form (transverse to the flow) and a smooth invariant probability measure λ. Our main technical result is the following: If the Anosov foliations are C∞, then either (1) the manifold is a transversely locally symmetric space, i.e. there is a flow-invariant C∞ affine connection ∇ on V such that ∇R ≡ 0, where R is the curvature tensor of ∇, and the torsion tensor T only has nonzero component along the flow direction, or (2) its Oseledec decomposition extends to a C∞ splitting of TV (defined everywhere on V) and for any invariant ergodic measure μ, there exists χμ > 0 such that the Lyapunov exponents are −2χμ, −χμ, 0, χμ, and 2χμ, μ-almost everywhere.As an application, we prove: Given a closed three-dimensional manifold of negative curvature, assume the horospheric foliations of its geodesic flow are C∞. Then, this flow is C∞ conjugate to the geodesic flow on a manifold of constant negative curvature.
A map with topological minimal self-joinings in the sense of del Junco
Authors: King Jonathan L. 
Published: September 2008

AbstractAndrés del Junco has proposed a definition of topological minimal self-joinings intended to parallel Dan Rudolph's measure-theoretic concept. By means of a rank-two ‘cutting and stacking’, this article constructs the first example of a system (a subshift) satisfying his proposed definition of 2-fold topological minimal self-joinings.The second part of the article shows that 2-fold topological minimal self-joinings does not imply 3-fold and that no map has 4-fold topological minimal self-joinings. This latter result follows from a generalization of a theorem of Schwartzman.
KAM theory for particles in periodic potentials
Authors: Levi Mark 
Published: September 2008

AbstractIt is shown that the system of the form x + V′ (x) = p (t) with periodic V and p and with (p) = 0 is near-integrable for large energies. In particular, most (in the sense of Lebesgue measure) fast solutions are quasiperiodic, provided V ∈ C(5) and p ∈ L1; furthermore, for any solution x(t) there exists a velocity bound c for all time: |x(t)| < c for all t ∈ R. For any real number r there exists a solution with that average velocity, and when r is rational, this solution can be chosen to be periodic.
Lorenz attractors through Šil'nikov-type bifurcation. Part I
Authors: Rychlik Marek Ryszard 
Published: September 2008

AbstractThe main result of this paper is a construction of geometric Lorenz attractors (as axiomatically defined by J. Guckenheimer) by means of an Ω-explosion. The unperturbed vector field on ℝ3is assumed to have a hyperbolic fixed point, whose eigenvalues satisfy the inequalities λ1> 0, λ2> 0, λ3> 0 and |λ2|>|λ1|>|λ3|. Moreover, the unstable manifold of the fixed point is supposed to form a double loop. Under some other natural assumptions a generic two-parameter family containing the unperturbed vector field contains geometric Lorenz attractors.A possible application of this result is a method of proving the existence of geometric Lorenz attractors in concrete families of differential equations. A detailed discussion of the method is in preparation and will be published as Part II.
The ergodic theorem for additive cocycles of ℤd or ℝd
Authors: Boivin Daniel , Derriennic Yves 
Published: September 2008

Let us consider (Ω, , μ, G) a measure-preserving dynamical system, (Ω, , μ) is a probability space. The group G, which is supposed to be either ℤd or ℝd (d ≥ 1), acts on Ω by measure-preserving transformations. This action is denned by a mapwhich is jointly measurable, such that Tx+y = TxTy and Txμ = μ
Floquet exponents for Jacobi fields
Authors: Craig Walter 
Published: September 2008

AbstractThis paper introduces a Riemannian invariant of a compact Riemannian manifold based on the spectral theory for the Jacobi field operator. It is the Floquet exponent for this operator, a purely dynamical quantity computable directly from the asymptotic behavior of Jacobi fields. We show that it is related to certain traces of the Green's function, and we derive further regularity and analyticity properties for the Green's function. In case the geodesic flow is ergodic, the Floquet exponent generalizes the measure entropy, and several entropy estimates follow. An asymptotic expansion of the Floquet exponent gives rise to a sequence of ‘Jacobi invariants’, which are related to the polynomial invariants of the K dV equation.
Uniqueness and ergodic properties of attractive g-measures
Authors: Hulse Paul 
Published: September 2008

AbstractWe consider g-measures for the shift on where S is a finite set. For a certain class of continuous g, two g-measures are identified; they are equal if and only if there is a unique g-measure. We prove that the natural extensions of these measures are Bernoulli. With a further restriction on g when S is a two-point set, we show that there is a unique g-measure. We also consider extensions of these results to the non-continuous case.
A method for proving that monotone twist maps have no invariant circles
Authors: Jungreis Irwin 
Published: September 2008

AbstractWe present an existence theorem for certain kinds of orbits of a monotone twist map and use it to obtain a criterion for proving that there are no invariant circles with a certain range of rotation numbers. We have used this criterion to prove (computer assisted) that the standard map has no invariant circles for several parameter values includingk= 0.9718.
The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains
Authors: Marcus Brian , Tuncel Selim 
Published: September 2008

AbstractWe study Markov chains via invariants constructed from periodic orbits. Canonical extensions, based on these invariants, are used to establish a constraint on the degree of finite-to-one block homomorphisms from one Markov chain to another. We construct a polytope from the normalized weights of periodic orbits. Using this polytope, we find canonically-defined induced Markov chains inside the original Markov chain. Each of the invariants associated with these Markov chains gives rise to a scaffold of invariants for the original Markov chain. This is used to obtain counterexamples to the finite equivalence conjecture and to a conjecture regarding finitary isomorphism with finite expected coding time. Also included are results related to the problem of minimality (with respect to block homomorphism) of Bernoulli shifts in the class of Markov chains with beta function equal to the beta function of the Bernoulli shift.
Resolving factor maps for shifts of finite type with equal entropy
Authors: Ashley Jonathan 
Published: September 2008

AbstractWe sharpen a result of Boyle, Marcus and Trow as follows. An aperiodic shift of finite type ΣAfactors onto another ΣBwith equal entropy by a 1-to-l almost everywhere right-closing map if and only if (1) the dimension group for ΣBis a quotient of that for ΣA; and (2) ΣAand ΣBsatisfy the trivial periodic point condition for existence of a shift-commuting map from ΣAto ΣB.
Iterates of meromorphic functions: I
Authors: Baker I. N. , Kotus J. , Yinian Lü 
Published: September 2008

AbstractFor functions meromorphic in the plane, apart from an exceptional case, the Julia set J is the closure of the set of all preimages of poles. The repelling periodic cycles are dense in J. In contrast with the case of transcendental entire functions, J may be a subset of a straight line and general classes of functions for which this is the case can be determined. J may also lie on a quasicircle through infinity which is not a straight line.
An extension of Šarkovskiư's Theorem to the n-od
Authors: Baldwin Stewart 
Published: September 2008

AbstractThe n-od is defined to be the set of all complex numbers z such that zn is a real number in the interval [0,1], i.e., a central point with n copies of the unit interval attached at their endpoints. Given a space X and a function f:X → X, Per (f) is defined to be the set {k: f has for a point of (least) period k, k a positive integer}. The main result of this paper is to give, for each n, a complete characterization of all possible sets Per (f), where f ranges over all continuous functions on the n-od.
The structure of automorphisms of real suspension flows
Authors: Keynes Harvey B. , Markley Nelson G. , Sears Michael 
Published: September 2008

AbstractThis paper is motivated by the connections between automorphisms of real suspension flows and ℝ2 suspension actions. Automorphisms which naturally lead to ℤ2-cocyles are examined from the viewpoint of covering theory in terms of an associated cylinder flow. A natural type of automorphisms (called simple) is analyzed via ergodic methods. It is shown that all automorphisms of suspensions built over minimal rotations on tori satisfy this condition. A more general approach using eigenfunctions extends this result to minimal affines, Furstenberg-type distal flows, certain nilmanifolds and a class of non-distal flows on the 2-torus.
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems
Authors: Nair R. 
Published: September 2008

In this paper we prove the following theorem.Theorem 1. For a measure-preserving system (X, β, μ, T) and a positive integer k, if f ∈ L2(X, β, μ), the averages,converge μ almost everywhere. Here p runs over the rational primes and πN denotes their number in [1, N].
The action at infinity of conservative groups of hyperbolic motions need not have atoms
Authors: Velling John A. , Matsuzaki Katsuhiko 
Published: September 2008

AbstractHerein the authors show that discrete groups of motions on Hn+1 may be conservative on Sn but have no positive measure ergodic components for this boundary action. An explicit example of such a group is given for H3 using the Apollonian circle packing of R2.
Chain recurrence and attraction in non-compact spaces
Authors: Hurley Mike 
Published: September 2008

AbstractIn the study of a dynamical systemf:X→Xgenerated by a continuous mapfon a compact metric spaceX, thechain recurrent setis an object of fundamental interest. This set was defined by C. Conley, who showed that it has two rather different looking, but equivalent, definitions: one given in terms of ‘approximate orbits’ through individual points (pseudo-orbits, or ε-chains), and the other given in terms of the global structure of the class of ‘attractors’ and ‘basins of attraction’ off. The first of these definitions generalizes directly to dynamical systems on any metric space, compact or not. The main purpose of this paper is to extend the second definition to non-compact spaces in such a way that it remains equivalent to the first.
Meromorphic multifunctions in complex dynamics
Authors: Baribeau L. , Ransford T. J. 
Published: September 2008

AbstractLet {RA} be an analytic family of rational maps and denote by j(λ) the Julia set of Rλ. We prove that the upper semicontinuous regularization j(λ) of j(λ) (which coincides with j(λ) for all λ in a dense open set) is a meromorphic multifunction, and give applications that illustrate the instability of Julia sets. In a similar vein, we also consider forward orbits of critical points and limit sets of Kleinian groups.
On the topology of manifolds with completely integrable geodesic flows
Authors: Paternain Gabriel P. 
Published: September 2008

AbstractWe show that if M is a compact simply connected Riemannian manifold whose geodesic flow is completely integrable with periodic integrals, then M is rationally elliptic, i.e. the rational homotopy of M is finite dimensional. We also show that rational ellipticity is shared by simply connected compact manifolds whose cotangent bundle admits a multiplicity free compact action that leaves invariant the Hamiltonian associated with some Riemannian metric. In particular it follows that if M is a Riemannian manifold whose geodesic flow is completely integrable by the Thimm method, then M is rationally elliptic. Other questions concerning the global behaviour of geodesics on homogeneous spaces are discussed.
A Wiener—Wintner property for the helical transform
Authors: Assani I. 
Published: September 2008

AbstractLet (X,ℱ,μ,ϕ) be a dynamical system ϕ is an invertible measure-preserving transformation on the measure space (X,ℱ,μ). We show that for each p, 1<p<∞,f ∈ Lp(μ) we can find a single null set off which exists for all ε ℝ.
Théorème ergodique pour les opérateurs positifs à moyennes bornées sur les espaces Lp(1 < p < ∞)
Authors: Brunel Antoine 
Published: September 2008

AbstractThe main result is a dominated ergodic theorem for a linear positive operator T on Lp(1 > p > ∞); the theorem holds if, and only if, T is Cesaro-bounded.
The topological entropy of cellular automata is uncomputable
Authors: Hurd Lyman P. , Kari Jarkko , Culik Karel 
Published: September 2008

AbstractThere is no algorithm which will take a description of a celluar automaton and determine whether it has zero topological entropy, or for any fixed ε > 0 compute its topological entropy to a tolerance e. Furthermore a set of aperiodic Wang tiles arising from Penrose's kite and dart tiles is used to demonstrate specific examples of cellular automata with a single periodic point but non-trivial non-wandering sets, which furthermore can be constructed to have arbitrarily high topological entropy.
Applications of the asymptotic range to analytic subalgebras of groupoid C*-algebras
Authors: Solel Baruch 
Published: September 2008

AbstractFor a 1-cocycle c on a principal r-discrete groupoid G, that vanishes only on the unit space of G, we show that the asymptotic range of c, , is an invariant for the total order c−1([0, ∞]). It follows that is also an invariant (with respect to isometric isomorphisms) of the triangular analytic algebra supported on c−1([0, ∞]). We also prove that if and only if the analytic algebra has a certain maximality property.
D-function of a minimal set and an extension of Sharkovskii's theorem to minimal sets
Authors: Ye Xiangdong 
Published: September 2008

AbstractLetXbe a compact Hausdorff space,f∈C0(X, X) andA⊂Xa minimal set off. We first introduce a new topological invariant, the D-function of a minimal set, by the investigation of the decomposition of the minimal set A under the action offn,n∈N. Then important properties about the invariant and the existence of minimal set with a given D-function in some subshift of finite type are discussed. Finally Sharkovskii's theorem is generalized to minimal sets of continuous mappings from the interval into itself.
Accessible saddles on fractal basin boundaries
Authors: Alligood Kathleen T. , Yorke James A. 
Published: September 2008

AbstractFor a homeomorphism of the plane, the basin of attraction of a fixed point attractor is open, connected, and simply-connected, and hence is homeomorphic to an open disk. The basin boundary, however, need not be homeomorphic to a circle. When it is not, it can contain periodic orbits of infinitely many different periods.
Bifurcations of dynamic rays in complex polynomials of degree two
Authors: Atela Pau 
Published: September 2008

AbstractIn the study of bifurcations of the family of degree-two complex polynomials, attention has been given mainly to parameter values within the Mandelbrot set M (e.g., connectedness of the Julia set and period doubling). The reason for this is that outside M, the Julia set is at all times a hyperbolic Cantor set. In this paper weconsider precisely this, values of the parameter in the complement of M. We find bifurcations occurring not on the Julia set itself but on the dynamic rays landing on itfrom infinity. As the parameter crosses the external rays of M, in the dynamic plane the points of the Julia set gain and lose dynamic rays. We describe these bifurcations with the aid of a family of circle maps and we study in detail the case of the fixed points.
Homeomorphic restrictions of smooth endomorphisms of an interval
Authors: Brucks Karen M. , Otero-Espinar Maria Victoria , Tresser Charles 
Published: September 2008

AbstractWe describe the asymptotic dynamics of homeomorphisms obtained as restrictions of generic C2 endomorphisms of an interval with finitely many critical points, all of which are non-flat, and with all periodic points hyperbolic. The ω -limit set of such a restricted endomorphism cannot be infinite, except when the restriction of the endomorphism to the closure of the orbit of some critical point is a minimal homeomorphism of an infinite set.
Random circle homeomorphisms
Authors: Downarowicz Tomasz , Mauldin R. Daniel , Warnock Tony T. 
Published: September 2008

AbstractWe investigate the behaviour of random homeomorphisms of the circle induced by composing a random homeomorphism of the interval with a randomly chosen rotation. These maps and their iterates are a.s. singular and for each rational number r in [0,1) it is shown that there is a positive probability of obtaining a map with rotation number r. For a ‘canonical’ method of producing these maps, bounds on the probability of obtaining a fixed point are obtained. We estimate this probability via computer simulations in three different ways. Simulations are also carried out for two periods. It remains unknown for this method whether a rational rotation number is obtained a.s.
An ergodic transformation with trivial Kakutani centralizer
Authors: Fieldsteel Adam , Rudolph Daniel J. 
Published: September 2008

AbstractGeneralizing from the centralizer of a measure-preserving dynamical system (X, ℬ, μ,T), one defines the Kakutani centralizerKC(T) of all ‘even Kakutani factor maps’ ϕ fromTto itself. Such a ϕ is a composition φ2ϕ1of an even Kakutani orbit equivalence ϕ1and a factor map ϕ2. We construct here an ergodicTacting on a nonatomic Lebesgue space (X,ℬ,μ) with the property that any ϕ ∈ KC(T) is invertible and of the formAll invertible maps of this form are automatically in KC(T) and hence for thisTthe Kakutani centralizer is as small as possible.
Matings of quadratic polynomials
Authors: Lei Tan 
Published: September 2008

AbstractWe apply Thurston's equivalence theory between dynamical systems of post-critically finite branched coverings and rational maps, to try to construct, from a pair of polynomials, a rational map. We prove that given two post-critically finite quadratic polynomials fc: z→z2+c and fc:z→ z2+c′, one can get a rational map if and only if c, c′ are not in conjugate limbs of the Mandelbrot set.
Existence of invariant tori in volume-preserving diffeomorphisms
Authors: Xia Zhihong 
Published: September 2008

AbstractIn this paper we consider certain volume-preserving diffeomorphisms on I × Tn, where I ∈ ℝ is a closed interval and Tn is an n-dimensional torus. We show that under certain non-degeneracy conditions, all of the maps sufficiently close to the integrable maps preserve a large set of n-dimensional invariant tori.
Finite beta-expansions
Authors: Frougny Christiane , Solomyak Boris 
Published: September 2008

AbstractWe characterize numbers having finite β-expansions where β belongs to a certain class of Pisot numbers: when the β-expansion of 1 is equal to a1a2…am, where a1≥a2≥…≥am≥1 and when the β-expansion of 1 is equal to t1t2…tm(tm+1)ω where t1≥t2≥…≥tm>tm+1≥1.
Entropy of snakes and the restricted variational principle
Authors: Misiurewicz M. , Tolosa J. 
Published: September 2008

AbstractFor interval maps, we define the entropy of a periodic orbit as the smallest topological entropy of a continuous interval map having this orbit. We consider the problem of computing the limit entropy of longer and longer periodic orbits with the same ‘pattern’ repeated over and over (one example of such orbits is what we call ‘snakes’). We get an answer in the form of a variational principle, where the supremum of metric entropies is taken only over those ergodic measures for which the integral of a certain function is zero. In a symmetric case, this gives a very easy method of computing this limit entropy. We briefly discuss applications to topological entropy of countable chains.
Singularities in the boundaries of local Siegel disks
Authors: Rogers James T. 
Published: September 2008

AbstractBounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show there are only two possibilities for the structure of the boundary of such a disk: either the boundary admits a nice decomposition onto a circle or it is an indecomposable continuum.
Variation of Hausdorff dimension of Julia sets
Authors: Ransford T. J. 
Published: September 2008

AbstractLet (Rλ)λ∈D be an analytic family of rational maps of degree d ≥ 2, where D is a simply connected domain in ℂ, and each Rλ is hyperbolic. Then the Hausdorff dimension δ(λ) of the Julia set of Rλ satisfieswhere ℋ is a collection of harmonic functions u on D. We examine some consequences of this, and show how it can be used to obtain estimates for the Hausdorff dimension of some particular Julia sets.
Rigidity of centralizers of real analytic diffeomorphisms
Authors: Rocha Jorge 
Published: September 2008

AbstractWe define a topology, denoted by Cω, on the space of real analytic diffeomorphisms and show that the elements of a residual (Baire second category) subset of diffeomorphisms that satisfy Axiom A and the Transversality Condition have a trivial centralizer; they only commute with their integer powers.
On the C2-creation of links of critical points
Authors: Contreras Gonzalo 
Published: September 2008

AbstractWe give necessary conditions for an endomorphism of the interval not to be C2+α-approximated by endomorphisms having a link between critical points. We apply these techniques to show that on a C2+α-generic set of unimodal maps the endomorphisms are either Axiom A or there exists an ergodic measure with zero Lyapunov exponent. Applying this result we prove the formula conjectured by Eckmann and Ruelle for the rate of escape of the complement of the basin of the sinks. We add some remarks on the C2-stability conjecture.
Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm
Authors: Ito S. , Keane M. , Ohtsuki M. 
Published: September 2008

AbstractWe prove that there exists a constant δ > 0 such that for almost every pair of numbers α and β there existsn0=n0(α,β) such that for anyn≥n0where the integerspn,qn,rnare provided by the modified Jacobi-Perron algorithm.