bluuebunny/crossref_metadata_2025_split huggingface dataset:
Periodic points and finite group actions on shifts of finite type
Authors: Fiebig Ulf-Rainer 
Published: September 2008

AbstractLet G be an abstract finite group. For an action α of G on a shift of finite type (SFT) S we introduce the periodic data of α, a computable finite-ordered set of complex polynomials. We show that two actions of G on possibly different SFTs are conjugate on periodic points iff their periodic data coincide. For each subgroup H of G the points fixed by α|H (the restriction of α to H) form a subsystem of S, which is of finite type. Our result shows that the zeta functions of these subsystems determine the conjugacy class (on periodic points) of α up to finitely many possibilities.The orbit space of a finite skew action on an SFT S, endowed with the homeomorphism induced by S, is shown to have a zeta function equal to the zeta function of an SFT which is a left-closing quotient of S. We show that this zeta function equals the zeta function of S iff the skew action is inert with respect to a certain power of S.Finally we consider functions of the periodic data as for example gyration numbers.
Orbital factor map
Authors: Hamachi Toshihiro , Kosaki Hideki 
Published: September 2008

AbstractFor a certain pair of discrete measured ergodic equivalence relations, we specify how one is imbedded into the other and obtain a factor and its subfactor. For this pair of factors index theory is developed. We obtain an index formula, an ‘extended’ relation corresponding to the basic extension, and so on. Our formulas as well as construction are very explicit and are given in terms of ‘measure theoretic’ data. We also present examples showing the contrast between type III0 index theory and type II1 (or IIIλ) index theory.
Poisson law for Axiom A diffeomorphisms
Authors: Hirata Masaki 
Published: September 2008

AbstractLet f be an Axiom A diffeomorphism, Ω its non wandering set, µ the Gibbs measure for the Lipschitz continuous potential. We consider the (suitably normalized) return times of the orbit to the ε-neighborhood of a point z ∈ Ω and prove that for µ-a.e. z the sequence of the normalized return times converges to the Poisson point process in finite dimensional distribution as ε → 0.
Cuntz—Krieger algebras associated with Fuchsian groups
Authors: Spielberg J. S. 
Published: September 2008

AbstractFor Fuchsian groups of the first kind containing parabolic elements, it is shown that the action on a suitable disconnection of the limit circle generates a Cuntz—Krieger C*-algebra. This clarifies and generalizes the situation of the subalgebra within O2, and provides a new proof of the simplicity and nuclearity of certain Cuntz—Krieger algebras. The proof relies on the Markov partition obtained from a suitable fundamental polygon for the group. Counter examples are given if an unsuitable fundamental polygon is used.
Weak disks of Denjoy minimal sets
Authors: Boyland Philip 
Published: September 2008

AbstractWe investigate the existence of Denjoy minimal sets and, more generally, strictly ergodic sets in the dynamics of iterated homeomorphisms. It is shown that for the full two-shift, the collection of such invariant sets with the weak topology contains topological balls of all finite dimensions. One implication is an analogous result that holds for diffeomorphisms with transverse homoclinic points. It is also shown that the union of Denjoy minimal sets is dense in the two-shift and that the set of unique probability measures supported on these sets is weakly dense in the set of all shift-invariant, Borel probability measures.
The enveloping semigroup of projective flows
Authors: Ellis Robert 
Published: September 2008

AbstractThe enveloping semigroup of a flow (X, T) has been used to study its dynamical properties. In this paper a detailed study is made of the class of enveloping semigroups which arise in the study of flows where T is a subgroup of GL(V) and X is the associated projective space, P(V).
Decomposing isometric extensions using group extensions
Authors: Forrest A. H. 
Published: September 2008

AbstractThis paper studies the structure of isometric extensions of compact metric topological dynamical systems with ℤ action and gives two decompositions of the general case to a more structured case. Suppose that Y → X is a M-isometric extension. An extension, Z, of Y is constructed which is also a G-isometric extension of X, where G is the group of isometries of M. The first construction shows that, provided that (X, T) is transitive, there are almost-automorphic extensions Y′ → Y and X′ → X, so that Y′ is homeomorphic to X′ × M and the natural projection Y′ → X′ is a group extension. The second shows that, provided that (X, T) is minimal, there is a G-action on Z which commutes with T and which preserves fibres and acts on each of them minimally. Each individual orbit closure, Za, in Z is a G′-isometric extension of X, where G′ is a subgroup of G, and there is a G′-action on Za which commutes with T, preserves fibres and acts minimally on each of them. Two illustrations are presented. Of the first: to reprove a result of Furstenberg; that every distal point is IP*-recurrent. Of the second: to describe the minimal subsets in isometric extensions of minimal topological dynamical systems.
A class ofC∞-stable foliations
Authors: Alaoui Aziz El Kacimi , Nicolau Marcel 
Published: September 2008

AbstractWe consider foliationsFobtained as the suspension of a linear foliationF0onnby means of a linear Anosov diffeomorphismAofnkeepingF0invariant. Under suitable conditions onAthe foliationsFare shown to beC∞-stable, i.e. any differentiable foliation which isC∞-close toFisC∞-conjugated toF. The proof relies on a criterium of stability stated by R. Hamilton.
Algorithmic complexity of points in dynamical systems
Authors: White Homer S. 
Published: September 2008

AbstractThis work is based on the author's dissertation. We examine the algorithmic complexity (in the sense of Kolmogorov and Chaitin) of the orbits of points in dynamical systems. Extending a theorem of A. A. Brudno, we note that for any ergodic invariant probability measure on a compact dynamical system, almost every trajectory has a limiting complexity equal to the entropy of the system. We use these results to show that for minimal dynamical systems, and for systems with the tracking property (a weaker version of specification), the set of points whose trajectories have upper complexity equal to the topological entropy is residual. We give an example of a topologically transitive system with positive entropy for which an uncountable open set of points has upper complexity equal to zero. We use techniques from universal data compression to prove a recurrence theorem: if a compact dynamical system has a unique measure of maximal entropy, then any point whose lower complexity is equal to the topological entropy is generic for that unique measure. Finally, we discuss algorithmic versions of the theorem of Kamae on preservation of the class of normal sequences under selection by sequences of zero Kamae-entropy.
Invariant measures for maps of the interval that do not have points of some period
Authors: Bobok Jozef , Kuchta Milan 
Published: September 2008

AbstractWe study invariant measures for a continuous function which maps a real interval into itself. We show that the ratio of the measures of the two subintervals into which it is divided by a fixed point is constrained by the the set of periods of periodic points. As a consequence of this we give a new forcing relation between periodic points.
Positivity conditions for polynomials
Authors: De Angelis Valerio 
Published: September 2008

AbstractWe study several notions of positivity for a class of real-valued functions of several variables that includes the Laurent polynomials. We show that Handelman's positivity condition is characterized by boundedness of the associated Legendre transformation, or boundedness of the entropy function, while another notion of positivity here introduced characterizes the mapping property of the Legendre transformation derived by Marcus and Tuncel for beta functions. Several examples are given to distinguish the various notions of positivity.
Ergodic sequences of averages of group representations
Authors: Lin Michael , Wittmann Rainer 
Published: September 2008

AbstractLet G be a locally compact σ -compact group with right Haar measure λ. A sequence {μn} of probabilities on G is called ergodic if for every f ∈ L1(G, λ) and t ∈ G we have ‖μn* (f − δt* f) ‖1 → 0. If T (t) is a bounded continuous representation of G by linear operators in a Banach space X, we define the μ,-average of T(t) by .
Holomorphic families of quasi-Fuchsian groups
Authors: Astala K. , Zinsmeister M. 
Published: September 2008

AbstractWe produce a holomorphic family of infinitely generated quasi-Fuchsian groups such that the Hausdorff dimension of the limit set L (Гλ) is identical to 1 for small λ, but strictly greater than 1 for λ ˜ 1. In particular, this shows that Hausdorff dimension does not depend real analytically on the parameter λ, contrary to the case of finitely generated groups.
Non-uniqueness of measures of maximal entropy for subshifts of finite type
Authors: Burton Robert , Steif Jeffrey E. 
Published: September 2008

AbstractIt is known that in one dimension an irreducible subshift of finite type has a unique measure of maximal entropy, the so-called Parry measure. Here we give a counterexample to this in higher dimensions. For this example, we also describe the geometric structure of the measures of maximal entropy and show that there are exactly two extremal measures.
The zeta function of the beta transformation
Authors: Flatto Leopold , Lagarias Jeffrey C. , Poonen Bjorn 
Published: September 2008

AbstractThe β-transformation ƒβ(x) = βx(mod 1), for β > 1, has a symbolic dynamics generalizing radix expansions to an integer base. Two important invariants of ƒβ are the (Artin-Mazur) zeta functionwhere Pk counts the number of fixed points of , and the lap-counting function where Lk counts the number of monotonic pieces of the kth iterate . For β-transformations these functions are related by ζβ(z) = (1 − z)Lβ(z). The function ζβ(z) is meromorphic in the unit disk, is holomorphic in {z: |z| < 1/β}, has a simple pole at z = 1/β, and has no other singularities with |z| = 1/β. Let M(β) denote the minimum modulus of any pole of ζβ(z) in |z| < 1 other than z = 1/β, and set M(β) = 1 if no other pole exists with |z| < 1. Then Pk = βk + O((M(β)−1+ε)k) for any ε > 0. This paper shows that M(β) is a continuous function, that ( for all β, and that An asymptotic formula is derived for M(β) as β → 1+, which implies that M(β) < 1 for all β in an interval (1, 1 + c0). The set is shown to have properties analogous to the set of Pisot numbers. It is closed, totally disconnected, has smallest element ≥ 1 + C0 and contains infinitely many β falling in each interval [n, n + 1) for n ∈ ℤ+. All known members of are algebraic integers which are either Pisot or Salem numbers.
Basins of attraction near homoclinic tangencies
Authors: Tatjer J.C. , Simó C. 
Published: September 2008

AbstractWe describe the behaviour of the basin of attraction of the attracting periodic points which appear near a non-degenerate tangential homoclinic point of a dissipative saddle fixed point for one-parameter families of planar diffeomorphisms. This behaviour depends on certain relations between the eigenvalues of the saddle point and on the geometry of the tangency.
Almost everywhere convergence of convolution powers
Authors: Bellow Alexandra , Jones Roger , Rosenblatt Joseph 
Published: September 2008

AbstractGiven an ergodic dynamical system (X,B,m, τ) and a probability measure μ on the integers, define for all f ∈ L1(X) The almost everywhere convergence of the convolution powers μnf(x) depends on the properties of μ. If μ has finite and then for all f ∈ Lp(X), 1< p < ∞, exists for a.e. x. However, if m2(μ) is finite and E(μ)≠0, then there exists E∈B such that a.e. and a.e. In the case when m2(μ) is infinite and E(μ)=0 we give examples for which we have divergence and other examples which show convergence is possible.
Topological conditions for the existence of invariant measures for unimodal maps
Authors: Bruin H. 
Published: September 2008

AbstractWe present a class of S-unimodal maps having an invariant measure which is absolutely continuous with respect to Lebesgue measure. This measure can often be proved to be finite. We give an example of a map which has such a finite measure and for which the lim inf of the derivatives of the iterates of the map in the critical value is finite. It will be shown that all topologically conjugate non-flat S-unimodal maps have the same properties.
One point intersections of middle-α Cantor sets
Authors: Kraft Roger L. 
Published: September 2008

AbstractFor α ∈ (0, 1), let Γα denote the middle-α Cantor set contained in the interval [0,1]. Let denote the set of all t∈[−1,1] such that Γα ∩(Γα+t)is a single point. Both a geometric and a symbolic description of each is presented. The symbolic description of each will be as a shift invariant subset of the one-sided two shift that is determined by inequalities. An equivalence relation is defined on the one-sided two shift and then a linear order relation is defined on the equivalence classes. This order relation on the equivalence classes describes how the sets shrink as a decreases from ⅓ to 0.
Periodic orbits of a dynamical system in a compound central field and a perturbed billiards system
Authors: Morita Takehiko 
Published: September 2008

AbstractWe consider a compound central field in the Euclidean plane which is governed by a finite number of bell-shaped potential functions with finite range. The study of the qualitative behavior of the Hamilton flow in such a potential field can be reduced to that of the so-called perturbed billiards system. The main result in this paper is the construction of a symbolic dynamics of the Hamilton flow by using the perturbed billiards system provided that the energy E > 0 is small enough. We also try to show an analogue of the prime number theorem for the closed orbits of the flow following ideas presented by Morita and Parry and Pollicott.
Regularity of the Anosov splitting and of horospheric foliations
Authors: Hasselblatt Boris 
Published: September 2008

Abstract‘Bunching’ conditions on an Anosov system guarantee the regularity of the Anosov splitting up toC2−ε. Open dense sets of symplectic Anosov systems and geodesic flows do not have Anosov splitting exceeding the asserted regularity. This is the first local construction of low-regularity examples.
The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
Authors: Homburg Ale Jan , Kokubu Hiroshi , Krupa Martin 
Published: September 2008

AbstractDeng has demonstrated a mechanism through which a perturbation of a vector field having an inclination-flip homoclinic orbit would have a Smale horseshoe. In this article we prove that if the eigenvalues of the saddle to which the homoclinic orbit is asymptotic satisfy the condition 2λu > min{−λs, λuu} then there are arbitrarily small perturbations of the vector field which possess a Smale horseshoe. Moreover we analyze a sequence of bifurcations leading to the annihilation of the horseshoe. This sequence contains, in particular, the points of existence of n-homoclinic orbits with arbitrary n.
Metric properties of non-renormalizableS-unimodal maps. Part I: Induced expansion and invariant measures
Authors: Jakobson Michael , Światek Grzegorz 
Published: September 2008

AbstractFor an arbitrary non-renormalizable unimodal map of the interval,f:I→I, with negative Schwarzian derivative, we construct a related mapFdefined on a countable union of intervals Δ. For each interval Δ,Frestricted to Δ is a diffeomorphism which coincides with some iterate offand whose range is a fixed subinterval ofI. IfFsatisfies conditions of the Folklore Theorem, we callfexpansion inducing. Letcbe a critical point off. Forfsatisfyingf″(c) ≠ 0, we give sufficient conditions for expansion inducing. One of the consequences of expansion inducing is that Milnor's conjecture holds forf: the ω-limit set of Lebesgue almost every point is the interval [f2,f(c)]. An important step in the proof is a starting condition in the box case: if for initial boxes the ratio of their sizes is small enough, then subsequent ratios decrease at least exponentially fast and expansion inducing follows.
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems
Authors: Katok Anatole , Burns Keith 
Published: September 2008

AbstractWe establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold aC∞Riemannian metric whose geodesic flow is Bernoulli.
Birkhoff-Hénon attractors for dissipative perturbations of area-preserving twist maps
Authors: Mora Leonardo 
Published: September 2008

AbstractWe prove that an area-preserving twist map having an invariant curve, can be approximated by a twist map exhibiting a Birkhoff-Hénon attractor. This is done by showing that the invariant curve can be perturbed into a saddle-node cycle with criticalities and by using a recent result reported by Diaz, Rocha and Viana.
Group-theoretic obstructions to integrability
Authors: Churchill R. C. , Rod D. L. , Singer M. F. 
Published: September 2008

AbstractLet V be a four-dimensional complex symplectic vector space. This paper classifies those connected linear algebraic subgroups of the symplectic group Sp(V) that admit two independent rational invariants. As an application we show the non integrability of a three degree of freedom Hamiltonian system.
Asymptotic stability of heteroclinic cycles in systems with symmetry
Authors: Krupa Martin , Melbourne Ian 
Published: September 2008

AbstractSystems possessing symmetries often admit heteroclinic cycles that persist under perturbations that respect the symmetry. The asymptotic stability of such cycles has previously been studied on an ad hoc basis by many authors. Sufficient conditions, but usually not necessary conditions, for the stability of these cycles have been obtained via a variety of different techniques.We begin a systematic investigation into the asymptotic stability of such cycles. A general sufficient condition for asymptotic stability is obtained, together with algebraic criteria for deciding when this condition is also necessary. These criteria are always satisfied in ℝ3 and often satisfied in higher dimensions. We end by applying our results to several higher-dimensional examples that occur in mode interactions with O(2) symmetry.
On the space of ergodic invariant measures of unipotent flows
Authors: Mozes Shahar , Shah Nimish 
Published: September 2008

AbstractLet G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.
Sur une notion d'autonomie de systèmes dynamiques, appliquée aux ensembles invariants des flots d' Anosov algébriques
Authors: Zeghib A. 
Published: September 2008

AbstractWe introduce a notion of autonomous dynamical systems which generalizes algebraic dynamical systems. We show by giving examples and by describing some properties that this generalization is not a trivial one. We apply the methods then developed to algebraic Anosov systems. We prove that a C1-submanifold of finite volume, which is invariant by an algebraic Anosov system is ‘essentially’ algebraic.
Some new rigidity results for stable orbit equivalence
Authors: Adams Scot 
Published: September 2008

AbstractBroadly speaking, we prove that an action of a group with very little commutativity cannot be stably orbit equivalent to an action of a group with enough commutativity, assuming both actions are free and finite measure preserving. For example, one group may be SL2(ℝ) and the other a group with infinite discrete center (e.g., the universal cover of SL2(ℝ)); I believe this is the first rigidity result of this type for a pair of simpleLie groups both of split rank one. Another example: one group may be any nonelementary word hyperbolic group, the other any group with infinite discrete center.
No division and the set of periods for tree maps
Authors: Alsedà Lluís , Ye Xiangdong 
Published: September 2008

AbstractWe extend the notion of no division for star maps to tree maps and prove that the set of periods of a tree map is cofinite if there exists some periodic orbit of the given map with period larger than one having no division. Using this result we obtain somesimple proofs of known results about the set of periods of a tree map. Also we show that this set is a union of initial segments of a finite number of linear orderings which depend only on the given tree minus a finite subset of ℕ.
Liapunov stability and adding machines
Authors: Buescu Jorge , Stewart Ian 
Published: September 2008

AbstractLet X be a locally connected locally compact metric space and f: X → X a continuous map. Let A be a compact transitive set under f. If A is asymptotically stable, then it has finitely many connected components, which are cyclically permuted. If it is Liapunov stable, then A may have infinitely many connected components. Our main result states that these form a Cantor set on which f is topologically conjugate to an adding machine. A number of consequences are derived, including a complete classification of compact transitive sets for continuous maps of the interval and the Liapunov instability of the invariant Cantor set of Denjoy maps of the circle.
On topological entropy of maps
Authors: Hurley Mike 
Published: September 2008

AbstractWe introduce an ‘entropy’ hm(f) for a continuous mapping of a compact metric space to itself which is denned in terms of (n, ∈)-separated subsets of inverse images of individual points. This invariant is compared with the inverse-image entropy h_(f) introduced recently by Langevin and Walczak. The two main results are: (1) the inequality hm(f) ≤ h(f) ≤ hm(f) + h_(f) relating hm, h_ and the topological entropy h(f); (2) if pseudo-orbits are used in place of orbits in the definition of hm then the quantity that results is equal to the topological entropy. We actually establish an inequality that at least formally is slightly stronger than (1) by defining a variant of h_ which we call hi; it is trivial to show that hi ≤ h_, and we show that h ≤ hi + hm, from which (1) follows.
Pseudogroups of isometries of ℝ: reconstruction of free actions on ℝ-trees
Authors: Gaboriau Damien , Levitt Gilbert , Paulin Frédéric 
Published: September 2008

AbstractRips' theorem about free actions on ℝ-trees relies on a careful analysis of finite systems of partial isometries of ℝ. We associate a free action on an ℝ-tree to any finite system of isometries without reflection. Any free action may be approximated (strongly in the sense of Gillet-Shalen) by actions arising in this way. Proofs involve the use, in an essential way, of separation properties of systems of isometries. We also interpret these finite systems of isometries as generating sets of pseudogroups of partial isometries between closed intervals of ℝ.
Persistence of homoclinic tangencies in higher dimensions
Authors: Romero Neptali 
Published: September 2008

AbstractIn this paper we extend to a very general context Newhouse's phenomenon concerning the persistence of homoclinic tangencies and the coexistence of infinitely many sinks. This is done using the corresponding results in codimension one recently provedby J. Palis and M. Viana, and in a reduction of codimension in the unfolding of homoclinic tangencies developed in the present paper.