bluuebunny/crossref_metadata_2025_split huggingface dataset:
Expanding endomorphisms of the circle revisited
Authors: Shub Michael , Sullivan Dennis 
Published: September 2008

AbstractTwo Cr, r ≥ 2, expanding maps of the circle which are absolutely continuously conjugate are Cr conjugate. Here ƒ and g: S1 → S1 are expanding if they stretch tangent vectors in some metric, and a conjugacy is an isomorphism h: S1 → S1 such that fh = hg.
On non-additive processes
Authors: Wacker Ulrich 
Published: September 2008

AbstractThe aim of this paper is to introduce and study the class of boundedly non-additive processes. The main result is the decomposition in theorem (2.1) and theorem (3.1), which says that a boundedly non-additive process is the sum of a non-positive subadditive, a non-negative superadditive and an additive process. By this decomposition we can extend the mean and local ergodic theorems for superadditive processes of M. A. Akcoglu and U. Krengel to boundedly non-additive processes. At the end of this paper some examples are given.
A quantitative version of the Kupka-Smale theorem
Authors: Yomdin Y. 
Published: September 2008

AbstractLet Mm be a compact, m-dimensional smooth manifold. The n-periodic point x of a diffeomorphism f: M → M is called γ-hyperbolic, for γ≥O, if the eigenvalues λj, of dfn(x) satisfy . We prove that any Ck-diffeomorphism f: M → M, k≥3, for any ε>0 can be ε-approximated in Ck-norm by fe: M → M such that for any n each n-periodic point of fe is (a(ε))nα - hyperbolic. Here and ao>0 depends on f
Anosov foliations and cohomology
Authors: Fried David 
Published: September 2008

AbstractThe cohomology action of an Anosov diffeomorphism on a nilmanifold resembles that of a Cartesian product map. Corresponding results hold for infranilmanifolds, giving an invariant bigrading of the cohomology and a fourfold symmetry that extends Poincaré duality. Holonomy invariant cocycles are applied to the action on first cohomology.
Resolving maps which commute with a power of the shift
Authors: Trow Paul 
Published: September 2008

AbstractIn this paper, we prove an extension of a theorem of Marcus, which says that every subshift of finite type of entropy log n, n an integer, factors onto the full n-shift. Let p(x) be a monic polynomial, irreducible over ℚ, whose coefficients (except for the leading coefficient) are non-positive integers. Suppose C(λ) is the companion matrix of p(x), where λ is the largest real root of p(x) (λ exists, by the Perron-Frobenius theorem). Then for any aperiodic, non-negative, integral matrix A, with Perron value λ, we give necessary and sufficient conditions for the existence of a positive integer n and a right-closing map f: ΣA→ΣC(λ) satisfying fσn = σnf (where σ is the shift map).
Chains, entropy, coding
Authors: Petersen Karl 
Published: September 2008

AbstractVarious definitions of the entropy for countable-state topological Markov chains are considered. Concrete examples show that these quantities do not coincide in general and can behave badly under nice maps. Certain restricted random walks which arise in a problem in magnetic recording provide interesting examples of chains. Factors of some of these chains have entropy equal to the growth rate of the number of periodic orbits, even though they contain no subshifts of finite type with positive entropy; others are almost sofic – they contain subshifts of finite type with entropy arbitrarily close to their own. Attempting to find the entropies of such subshifts of finite type motivates the method of entropy computation by loop analysis, in which it is not necessary to write down any matrices or evaluate any determinants. A method for variable-length encoding into these systems is proposed, and some of the smaller subshifts of finite type inside these systems are displayed.
Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable
Authors: Host B. 
Published: September 2008

AbstractParmi les systèmes dynamiques définis par des substitutions, les mieux connus sont ceux qui proviennent de substitutions à longueur constante. F. M. Dekking [1] a déterminé les valeurs propres de ces systèmes, et, plus récemment, M. Queffelec a étudié leur type spectral maximal. On se propose ici de déterminer les valeurs propres de ces systèmes dans le cas général des substitutions à longueur variable; dans cette direction, un résultat partiel a été obtenu par J. C. Martin [3] dans le cas des substitutions de 2 lettres, pour les valeurs propres correspondant à des fonctions propres continues.
The Connes spectrum for actions of Abelian groups on continuous-trace algebras
Authors: Hurder Steven , Olesen Dorte , Raeburn Iain , Rosenberg Jonathan 
Published: September 2008

AbstractWe study the various notions of spectrum for an action α of a locally compact abelian groupGon a typeIC*-algebraA, and discuss how these are related to the structure of the crossed productA⋊αG. In the case whereAhas continuous trace and the action ofGon Â is minimal, we completely describe the ideal structure of the crossed product. A key role is played by the restriction of α to a certain ‘symmetrizer subgroup’Sof the common stabilizer inGof the points of Â. We show by example that, contrary to a conjecture of Bratteli, it is possble forA⋊Gto be primitive but not simple, provided thatSis not discrete. In such cases, the Connes spectrum Γ(α) differs from the strong Connes spectrumof Kishimoto. The counterexamples come from subtle phenomena in topological dynamics.
The spectra of topological Markov shifts
Authors: Lind D. A. 
Published: September 2008

AbstractFor every Perron number λ we construct an infinite collection of topological Markov shifts with entropy log λ whose spectra are disjoint except for the necessary conjugates of λ. This is used to show that Marcus' theorem about every Markov shift of entropy log n factoring onto the full n-shift does not extend to certain entropy values.
The algebraic-geometric AKNS potentials
Authors: de Concini Corrado , Johnson Russell A. 
Published: September 2008

AbstractWe characterize the algebraic-geometric potentials for the Schrödinger and AKNS operators using the Weyl m-functions and the Floquet exponent for these operators. The characterization is this: among random ergodic Schrödinger operators, the alebraic-geometric potentials are those for which (i) the spectrum is a union of finitely many intervals (or bands); (ii) the Lyapounov exponent vanishes on the spectrum.
Topological dynamics and ergodic theory
Authors: Ellis Robert 
Published: September 2008

AbstractIt is shown that when viewed properly some concepts in topological dynamics and ergodic theory are not merely analogous but equivalent. Also the Mackey-Halmos-von Neumann theorem on ergodic processes with discrete spectrum is generalized and an account of the Mackey-Zimmer theory of minimal cocycles is given in a more general setting.
Semi-rigidity of horocycle flows over compact surfaces of variable negative curvature
Authors: Feldman J. , Ornstein D. 
Published: September 2008

AbstractLet g be the geodesic flow on the unit tangent bundle of a C3 compact surface of negative curvature. Let μ be the g-invariant measure of maximal entropy. Let h be a uniformly parametrized flow along the horocycle foliation, i.e., such a flow exists, leaves μ invariant, and is unique up to constant scaling of the parameter (Margulis). We show that any measure-theoretic conjugacy: (h, μ) → (h′, μ′) is a.e. of the form θ, where θ is a homeomorphic conjugacy: g → g′. Furthermore, any homeomorphic conjugacy g → g′; must be a C1 diffeomorphism.
On Gibbs and equilibrium states
Authors: Haydn Nicolai T. A. 
Published: September 2008

AbstractRuelle and Capocaccia gave a new definition of Gibbs states on Smale spaces. Equilibrium states of suitable functions thereon are known to be Gibbs states. The converse is discussed in this paper, where the problem is reduced to shift spaces and solved there by constructing suitable conjugating homeomorphisms in order to verify the conditions for Gibbs states which Bowen gave for shift spaces, where the equivalence to equilibrium states is known.
The C1,1 conclusions in Gromov's theory
Authors: Pugh Charles C. 
Published: September 2008

AbstractAccording to M. Gromov, any sequence of Riemann manifolds with uniformly bounded geometry has a subsequence that converges to a limit. It is shown here that this limit Riemann structure is Lipschitz, generates a Lipschitz geodesic flow, and consequently, as Gromov asserted, the limit distance function is of class C1,1. Sharpness of the results is discussed. A simple, extrinsic proof of Gromov's Theorem is included.
The ordering on permutations induced by continuous maps of the real line
Authors: Bernhardt Chris 
Published: September 2008

AbstractContinuous maps from the real line to itself give, in a natural way, a partial ordering of permutations. This ordering restricted to cycles is studied.Necessary and sufficient conditions are given for a cycle to have an immediate predecessor. When a cycle has an immediate predecessor it is unique; it is shown how to construct it. Every cycle has immediate successors; it is shown how to construct them.
Eventually positive matrices with rational eigenvectors
Authors: Handelman David 
Published: September 2008

AbstractLet A be an n × n real matrix; sufficient conditions were previously worked out, assuming non-commensurability of eigenvectors, for A to be SL(n, )-conjugate to a matrix all sufficiently large powers of which have strictly positive entries. We show that when the ‘large’ eigenvectors are commensurable and satisfy the obvious necessary conditions, then A is also going to be so conjugate. In particular, we deduce, if A is a rational matrix with large eigenvalue exceeding 1 and of multiplicity one, then A is algebraically shift equivalent to an eventually positive matrix, using only integer rectangular matrices.
Necessary and sufficient conditions for a maximal ergodic theorem along subsequences
Authors: Jones Roger L. 
Published: September 2008

AbstractLet T be an ergodic measure preserving point transformation from a probability space X onto itself. Assume that is an increasing sequence of subsets of the positive integers. Conditions are given which are sufficient for the ergodic maximal function associated with these subsets to be weak type (p, p). These conditions are shown to be both necessary and sufficient for a larger two-sided maximal function. The conditions are in the form of covering lemmas for the integers.
A rank-one, rigid, simple, prime map
Authors: del Junco A. , Rudolph D. J. 
Published: September 2008

AbstractWe construct a rank-1 mapTsimilar to Chacon's map [C], [JRS], but with 2n+1n-blocks in an (n + 1)-block and a single spacer in the middle. HenceTis rigid and the centralizer ofT, C(T), is uncountable. We showTis simple [V], [JR], and hence any factor ofTis the algebra of invariant sets of some weakly compact subgroup ofC(T). We showC(T) has no such subgroups and henceTis prime. Lastly we show thatTis graphic in the sense of [AM].
Markov measures determine the zeta function
Authors: Tuncel Selim 
Published: September 2008

AbstractWith the purpose of understanding when two subshifts of finite type are equivalent from the point of view of their spaces of Markov measures we propose the notion of Markov equivalence. We show that a Markov equivalence must respect the cycles (periodic orbits) of the subshifts. In particular, Markov equivalent subshifts of finite type have the same zeta function.
An ergodic theorem for iterated maps
Authors: Elton John H. 
Published: September 2008

AbstractConsider a Markov process on a locally compact metric space arising from iteratively applying maps chosen randomly from a finite set of Lipschitz maps which, on the average, contract between any two points (no map need be a global contraction). The distribution of the maps is allowed to depend on current position, with mild restrictions. Such processes have unique stationary initial distribution [BE], [BDEG].We show that, starting at any point, time averages along trajectories of the process converge almost surely to a constant independent of the starting point. This has applications to computer graphics.
Invariant subsets of expanding mappings of the circle
Authors: Urbański Mariusz 
Published: September 2008

AbstractThe continuity of Hausdorff dimension of closed invariant subsetsKof aC2-expanding mappinggof the circle is investigated. Ifg/Ksatisfies the specification property then the equilibrium states of Hölder continuous functions are studied. It is proved that iffis a piecewise monotone continuous mapping of a compact interval and φ a continuous function withP(f,φ)> sup(φ), then the pressureP(f,φ) is attained on one-dimensional ‘Smale's horseshoes’, and some results of Misiurewicz and Szlenk [M−Sz] are extended to the case of pressure.
Cohomology of chain recurrent sets
Authors: Hirsch Morris W. , Pugh Charles C. 
Published: September 2008

AbstractLet ϕ be a flow on a compact metric space Λ and let p ∈ Λ be chain recurrent. We show that (Λ; ℝ) ≠ 0 if dimp Λ = 1 or if p belongs to a section of ϕ. Applications to planar flows and to smooth flows are given.
Another proof of Jakobson's Theorem and related results
Authors: Rychlik Marek Ryszard 
Published: September 2008

AbstractThe author shows that any family C2-close to fα(x) = 1 − αx2(2 − ε ≤ α ≤ 2) satisfies Jakobson's theorem: For a positive measure set of α the transformation fα has an absolutely continuous invariant measure. He also indicates some generalizations.
Asymptotic behaviour of iterated piecewise monotone maps
Authors: Willms Jürgen 
Published: September 2008

AbstractIn this paper the asymptotic behaviour of piecewise monotone functions f: I → I with a finite number of discontinuities is studied (where I ⊆ ℝ is a compact interval). It is shown that there is a finite number of f-almost-invariant subsets C1,…, Cr, R1,…, Rs, where each Ci is a disjoint union of closed intervals and each Rj is a Cantor-like subset of I, such that if x is a ‘typical’ point in I (in a topological sense) then exactly one of the following three possibilities will happen:(1) {fn (x)}n ≥ 0 eventually ends up in some Ci.(2) {fn (x)}n ≥ 0 is attracted to some Rj.(3) {fn (x): n ≥ 0} is contained in an open, invariant set Z ⊆ I, which is such that for each n ≥ 1 fn is monotone and continuous on each connected component of Z.Moreover, f acts topologically transitively on each Ci and minimally on each Rj. Furthermore, it is shown how the sets C1,…, Cr, R1,…, Rs can be constructed. Finally, our results are applied to some examples.
Measure theoretic entropy of the system of hard spheres
Authors: Wojtkowski Maciej P. 
Published: September 2008

AbstractWe estimate from below the measure theoretic entropy of the system of spheres interacting by elastic collisions. We find the asymptotics of the entropy in the case of two disks on atoms as the radius increases. We establish that high density leads to large entropy. We introduce a general estimate for Lyapunov exponents in the case of special symplectic matrices.
Minimal flows of finite almost periodic rank
Authors: Auslander Joseph , Markley Nelson 
Published: September 2008

AbstractThe totally minimal flow (X, T) is said to have finite almost periodic rank if there is a positive integer n such that whenever (x1, x2,…, xn+1) is an almost periodic point of the product flow (Xn+1, T×…×T) then, for some i≠j, xi, and xj are in the same orbit. The rank of (X, T) is the smallest such integer. If (Y, S) is a graphic flow, (Y, Sn) has rank |n| and it is shown that every finite rank flow has, modulo a proximal extension, a graphic power factor. Various classes of finite rank flows are defined, and characterized in terms of their Ellis groups. There are four disjoint types which have basic structural differences.
On ergodic foliations
Authors: Park Kyewon 
Published: September 2008

AbstractWe define an ergodic ℤ-foliation and show that it can be realized as a quotient space of the ‘covering space’. The covering space has two actions, T and S, where T is a ℤ-action, S is a map of order two, and S and T skew-commute; that is, STS = T−1. We study the isometry between two foliations via the isomorphism between two bigger group actions in the covering spaces. Properties of an ergodic foliation are studied in a way similar to the study of an ergodic action. We construct a counterexample of a K-automorphism to show that, unlike Bernoulli automorphisms, ℤ-actions do not completely determine ℤ-foliations.
Subrelations of ergodic equivalence relations
Authors: Feldman J. , Sutherland C. E. , Zimmer R. J. 
Published: September 2008

AbstractWe introduce a notion of normality for a nested pair of (ergodic) discrete measured equivalence relations of type II1. Such pairs are characterized by a groupQwhich serves as a quotient for the pair, or by the ability to synthesize the larger relation from the smaller and an action (modulo inner automorphisms) ofQon it; in the case whereQis amenable, one can work with a genuine action. We classify ergodic subrelations of finite index, and arbitrary normal subrelations, of the unique amenable relation of type II1. We also give a number of rigidity results; for example, if an equivalence relation is generated by a free II1-action of a lattice in a higher rank simple connected non-compact Lie group with finite centre, the only normal ergodic subrelations are of finite index, and the only strongly normal, amenable subrelations are finite.
The singularity spectrumf(α) for cookie-cutters
Authors: Rand D. A. 
Published: September 2008

AbstractI use a thermodynamic formalism to study the spectrumf(α) which characterises the large fluctuations of pointwise dimension in a Gibbs state supported on a hyperbolic cookie-cutter. Amongst other things, it is proved thatf(α) is the Hausdorff dimension of the set of points with pointwise dimension α, thatf(α) is real-analytic and that its Legendre transform τ(q) is related to the Renyi dimensionDqof the Gibbs state by the formula (1 −q)Dq= τ(q).
Automorphisms of compact groups
Authors: Kitchens Bruce , Schmidt Klaus 
Published: September 2008

AbstractWe study finitely generated, abelian groups Γ of continuous automorphisms of a compact, metrizable group X and introduce the descending chain condition for such pairs (X, Γ). If Γ acts expansively on X then (X, Γ) satisfies the descending chain condition, and (X, Γ) satisfies the descending chain condition if and only if it is algebraically and topologically isomorphic to a closed, shift-invariant subgroup of GΓ, where G is a compact Lie group. Furthermore every such subgroup of GΓ is a (higher dimensional) Markov shift whose alphabet is a compact Lie group. By using the descending chain condition we prove, for example, that the set of Γ-periodic points is dense in X whenever Γ acts expansively on X. Furthermore, if X is a compact group and (X, Γ) satisfies the descending chain condition, then every ergodic element of Γ has a dense set of periodic points. Finally we give an algebraic description of pairs (X, Γ) satisfying the descending chain condition under the assumption that X is abelian.
Trees and amenable equivalence relations
Authors: Adams Scot 
Published: September 2008

AbstractLet R be a Borel equivalence relation with countable equivalence classes on a measure space M. Intuitively, a ‘treeing’ of R is a measurably-varying way of makin each equivalence class into the vertices of a tree. We make this definition rigorous. We prove that if each equivalence class becomes a tree with polynomial growth, then the equivalence relation is amenable. We prove that if the equivalence relation is finite measure-preserving and amenable, then almost every tree (i.e., equivalence class) must have one or two ends.
Quasi-transversal saddle-node bifurcation on surfaces
Authors: Beloqui J. , Pacifico M. J. 
Published: September 2008

AbstractIn this paper we give a complete set of invariants (moduli) for mild and strong semilocal equivalence for certain two parameter families of diffeomorphisms on surfaces. These families exhibit a quasi-transversal saddle-connection between a saddle-node and a hyperbolic periodic point.
Suspensions of topological transformation groups
Authors: Ellis David B. 
Published: September 2008

AbstractLet S be a subgroup of a topological group T, and suppose that S acts on a space X. One can form a T-transformation group (X ×sT, T) called the suspension of the S-transformation group (X, S). In this paper we study the relationship between the dynamical properties of (X, S) and those of its suspension when S is syndetic in T. The main tool used in this study is a notion of the group of a minimal flow (X, T) which is sensitive to the topology on the group T. We are able, using this group and the enveloping semigroup to obtain results on which T-transformation groups can be realized as suspensions of S-transformation groups, and give conditions under which the suspension of an equicontinuous S-flow is an equicontinuous T-flow.
Invariant curves around a parabolic fixed point at infinity
Authors: Aharonov Dov , Elias Uri 
Published: September 2008

AbstractThe stability of a fixed point of an area-preserving transformation in the plane is characterized by the invariant curves which surround it. The existence of invariant curves had been extensively studied for elliptic fixed points. Here we study the similar problem for parabolic fixed points. In particular we are interested in the case where the fixed point is at infinity.
Homotopical stability of pseudo-Anosov diffeomorphisms
Authors: Fathi Albert 
Published: September 2008

AbstractWe show that the pseudo-Anosov diflEeomorphisms have a kind of stability even outside their own homotopy class, this generalizes some results of Lewowicz and Handel. As a corollary, we show that two pseudo-Anosov maps, with the same dilatation coefficient, which are semi-conjugate on the π1 level are also semiconjugate as dynamical systems by a map which is a ramified cover.
Approximations of continuous functions by squares
Authors: Humke Paul D. , Laczkovich Miklós 
Published: September 2008

AbstractLet C denote the space of continuous functions mapping [0,1] into itself and endowed with the sup metric. It has been shown that C2 = {f ∘ f: ∈ C} is an analytic but non-Borel subset of C. This implies that there is no simple geometric characterization for a function being a square. In this paper we consider the problem of characterizing those functions which can be approximated by squares. In the first section we prove that any continuous function mapping a closed proper subset of [0,1 ] into [0,1 ] can be extended to a square. In particular this shows that C2 is Lp dense in C. On the other hand, C2 does not contain a ball when C is endowed with the sup metric. In the second section we prove that no strictly decreasing function can be uniformly approximated by squares, although the distance between the class of strictly decreasing functions and C2 is zero. In the last section we investigate the function f(x) = 1 − x and show that for every g ∈ C and that ¼ cannot be improved.
Approximate solutions of cohomological equations associated with some Anosov flows
Authors: Katok Svetlana 
Published: September 2008

AbstractThe Livshitz theorem reported in 1971 asserts that any C1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a ‘finite version’ of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.
Open index pairs, the fixed point index and rationality of zeta functions
Authors: Mrozek Marian 
Published: September 2008

AbstractWe define open index pairs of an isolated invariant set, prove their existence and compute the fixed point index of an isolating neighbourhood in terms of the Lefschetz number of a certain map associated with the open index pair. We use this to establish rationality of zeta functions and Lefschetz zeta functions.