bluuebunny/crossref_metadata_2025_split huggingface dataset:
Global dynamical properties of Euler and backward Euler
Authors: Hockett Kevin 
Published: September 2008

AbstractWe investigate the global dynamics of both the Euler and backward Euler algorithms as applied to polynomial vector fields on the Riemann sphere = ℂ ∪ {∞}. The geometry and dynamics of solutions at infinity is seen to play an important role in organizing the global dynamics of the flow, and we show how to modify both algorithms to account for this structure, thereby obtaining global approximations to the flow.
Mixing sets and relative entropies for higher-dimensional Markov shifts
Authors: Kitchens Bruce , Schmidt Klaus 
Published: September 2008

AbstractWe consider certain measurable isomorphism invariants for measure-preserving ℤd-actions on probability spaces, compute them for a class of d-dimensional Markov shifts, and use them to prove that some of these examples are non-isomorphic. The invariants under discussion are of three kinds: the first is associated with the higher-order mixing behaviour of the ℤd-action, and is related—in this class of examples—to an an arithmetical result by David Masser, the second arises from certain relative entropies associated with the ℤd-action, and the third is a collection of canonical invariant σ-algebras. The results of this paper are generalizations of earlier results by Kitchens and Schmidt, and we include a proof of David Masser's unpublished theorem.
Multiphase averaging for generalized flows on manifolds
Authors: Dumas H. S. , Golse F. , Lochak P. 
Published: September 2008

AbstractWe present a new proof of a strengthened version of Anosov's multiphase averaging theorem, originally stated for systems of ODEs with slow variables evolving in Rm and fast variables evolving on a smooth immersed manifold. Our result allows the fast variables to belong to an arbitrary smooth compact Riemannian manifold, and the vector field to have only Sobolev regularity. This is accomplished using normal form techniques adapted to a slightly generalized version of the DiPema-Lions theory of generalized flows for ODEs.
On the class of multipliers for W⊥
Authors: Glasner Eli 
Published: September 2008

AbstractLet W⊥ be the class of all ergodic measure-preserving transformations (systems), which are disjoint from every weakly mixing system. Let M(W⊥) be the class of multipliers for W⊥; i.e. the class of all systems (X, μ, T) in W⊥ such that for every system (Y, ν, T) ∈ W⊥ and every ergodic joining λ of X and Y, the system (X × Y, λ, T × T) is also in W⊥. Well known results on disjointness show that the class D of ergodic distal systems, is a subclass of M(W⊥). Thus one has D ⊂ M(W⊥) ⊂ W⊥. Glasner and Weiss have shown that D ≠ W⊥. The purpose of this paper is to also show that D ≠ M(W⊥). The question whether M(W⊥) = W⊥ remains open.
Ergodic theorems for random sets with density zero
Authors: Huang Yenkun 
Published: September 2008

AbstractWe generalize a result of Bourgain and a result of Huang. We also give a positive solution to A. Bellow's question: the a.e. convergence of the averages for σn = 1/n. On the other hand, we establish a sufficient and necessary condition for random sets in Z+ with asymptotic density zero which almost surely satisfy a mean ergodic theorem.
Topological rigidity of strong stable foliations for Cartan actions
Authors: Hurder Steven 
Published: September 2008

AbstractWe show that the strongest stable foliations associated with the generators of a Cartan action on a compact infra-nilmanifold are invaraint under topological conjugacy. This has the corollary that a Cartan action on a compact infra-nilmanifold with constant exponents is smoothly conjugate to an affine action.
Distortion results and invariant Cantor sets of unimodal maps
Authors: Martens Marco 
Published: September 2008

AbstractA distortion theory is developed for S-unimodal maps. It will be used to get some geometric understanding of invariant Cantor sets. In particular attracting Cantor sets turn out to have Lebesgue measure zero. Furthermore the ergodic behavior of S-unimodal maps is classified according to a distortion property, called the Markov-property.
Properties of invariant measures for piecewise expanding one-dimensional transformations with summable oscillations of derivative
Authors: Góra Pawel 
Published: September 2008

AbstractWe study the properties of absolutely continuous invariant measures for one-dimensional transformations satisfying Schmitt's condition. We prove existence, constrictiveness of the induced Perron-Frobenius operator, openness of supports, estimate on a number of ergodic components, exponential decay of correlation, Bernoulli property, etc.
Convergence and divergence of ergodic averages
Authors: Jones Roger L. , Wierdl Mate 
Published: September 2008

AbstractIn this paper we consider almost everywhere convergence and divergence properties of various ergodic averages. A general method is given which can be used to construct averages for which a.e. convergence fails, and to show divergence (and in some cases ‘strong sweeping out’) for large classes of ergodic averages. We also show that there are sequences with the gaps between successive terms converging to zero, but such that the Cesaro averages obtained by sampling a flow along these sequences of times converge a.e. for all f∈L1(X).
Symbolic dynamics for angle-doubling on the circle III. Sturmian sequences and the quadratic map
Authors: Keller Karsten 
Published: September 2008

AbstractBy the theory of Douady and Hubbard, the structure of Julia sets of quadratic maps is tightly connected with the angle-doubling maphon the circleT. In particular, a connected and locally connected Julia set can be considered as a topological factorT/ ≈ ofTwith respect to a specialh-invariant equivalence relation ≈ onT, which is called Julia equivalence by Keller. Following an idea of Thurston, Bandt and Keller have investigated a map α →αfromTonto the set of all Julia equivalences, which gives a natural abstract description of the Mandelbrot set. By the use of a symbol sequence called the kneading sequence of the point α, they gave a topological classification of the abstract Julia setsT/α. It turns out thatT/αcontains simple closed curves iff the point α has a periodic kneading sequence. The present article characterizes the set of points possessing a periodic kneading sequence and discusses this set in relation to Julia sets and to the Mandelbrot set.
Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’
Authors: Hu Huyi , Young Lai-Sang 
Published: September 2008

AbstractThe purpose of this paper is to present some simple examples that are hyperbolic everywhere except at one point, but which do not admit SBR measures. Each example has a fixed point at which the larger eigenvalue is equal to one and the smaller eigenvalue is less than one.
Fibonacci maps re(aℓ)visited
Authors: Keller Gerhard , Nowicki Tomasz 
Published: September 2008

AbstractWe prove that unimodal Fibonacci maps with negative Schwarzian derivative and a critical point of order ℓ have a finite absolutely continuous invariant measure if ℓ ∈ (1 ℓ1) where ℓ1 is some number strictly greater than 2. This extends results of Lyubich and Milnor for the case ℓ = 2.
Caractérisation des flots d' Anosov en dimension 3 par leurs feuilletages faibles
Authors: Barbot Thierry 
Published: September 2008

AbstractWe consider Anosov flows on closed 3-manifolds. We show that if such a flow admits a weak foliation whose lifting in the universal covering is a product foliation, thenit is characterized up to topological equivalence by its weak stable foliation up to topological conjugacy. As a corollary we obtain that, up to topological equivalence and finite coverings, suspensions and geodesic flows are the unique Anosov flows on closed 3-manifolds whose weak stable foliations are transversely projective.
Robust nonhyperbolic dynamics and heterodimensional cycles
Authors: Díaz Lorenzo J. 
Published: September 2008

AbstractWe describe an open set A of arcs of diffeomorphisms bifurcating through the creation of heterodimensional cycles for which every diffeomorphism after the bifurcation is nonhyperbolic or unstable. We also prove that generically in A the borning nonwandering set is transitive and local maximal for a full (Lebesgue) set of parameter values.
A note on transitive flows
Authors: Lawrence Deborah A. , Thomas Edward S. 
Published: September 2008

AbstractIn this article, we study transitive flows on manifolds or on manifold-like phase spaces. These are flows in which at least one orbit is dense. By quantifying the nature of the set of dense orbits, a variety of transitivity types is obtained. We explore conditions under which products or ‘scaled’ products of transitive flows are again transitive. We also investigate a connection between transitivity and topologically strong mixing.
Ruelle's transfer operator for random subshifts of finite type
Authors: Bogenschütz Thomas , Gundlach Volker Mathias 
Published: September 2008

AbstractWe consider a Ruelle—Perron—Frobenius type of selection procedure for probability measures that are invariant under random subshifts of finite type. In particular we prove that for a class of random functions this method leads to a unique probability exhibiting properties that justify the names Gibbs measure and equilibrium states. In order to do this we introduce the notion of bundle random dynamical systems and provide a theory for their invariant measures as well as give a precise definition of Gibbs measures.
The Hausdorff dimension of certain solenoids
Authors: Bothe H. G. 
Published: September 2008

AbstractFor the solid torus V = S1 × and a C1 embedding f: V → V given by with dϕ/dt > 1, 0 < λi(t) < 1 the attractor Λ = ∩i = 0∞fi(V) is a solenoid, and for each disk D(t) = {t} × (t ∈ S1) the intersection Λ(t) = Λ ∩ D(t) is a Cantor set. It is the aim of the paper to find conditions under which the Hausdorff dimension of Λ(t) is independent of t and determined by where the real numbers pi are characterized by the condition that the pressure of the function log : S1 → ℝ with respect to the expanding mapping ϕ: S1 → S1 becomes zero. (There are two further characterizations of these numbers.)It is proved that (0.1) holds provided λ1, λ2 are sufficiently small and Λ satisfies a condition called intrinsic transverseness. Then it is shown that in the C1 space of all embeddings f with sup λi > Θ−2 (Θ the mapping degree of ϕ: S1 → S1) all those f which have an intrinsically transverse attractor Λ form an open and dense subset.
Common extensions and hyperbolic factor maps for coded systems
Authors: Fiebig Doris 
Published: September 2008

AbstractThe classification of dynamical systems by the existence of certain common extensions has been carried out very successfully in the class of shifts of finite type (‘finite equivalence’, ‘almost topological conjugacy‘). We consider generalizations of these notions in the class of coded systems. Topological entropy is shown to be a complete invariant for the existence of a common coded entropy preserving extension. In contrast to the shift of finite type setting, this extension cannot be made bounded-to-1 in general. Common extensions with hyperbolic factor maps lead to a version of almost topological conjugacy for coded systems.
A subshift of finite type that is equivalent to the Ising model
Authors: Häggström Olle 
Published: September 2008

AbstractFor the Ising model with rational parameters we show how to construct a subshift of finite type that is equivalent to this Ising model, in that the translation invariant Gibbs measures for the Ising model and the measures of maximal entropy for the subshift of finite type can be identified in a natural way. This is generalized to the non-translation invariant case as well. We also show how to construct, given any H > 0, an ergodic measure of maximal entropy for a subshift of finite type and a continuous factor, such that the factor has entropy H.
Higher cohomology for Abelian groups of toral automorphisms
Authors: Katok Anatole , Katok Svetlana 
Published: September 2008

AbstractWe give a complete description of smooth untwisted cohomology with coefficients in ℝl for ℤk-actions by hyperbolic automorphisms of a torus. For 1 ≤ n ≤ k − 1 the nth cohomology trivializes, i.e. every cocycle is cohomologous to a constant cocycle via a smooth coboundary. For n = k a counterpart of the classical Livshitz Theorem holds: the cohomology class of a smooth k-cocycle is determined by periodic data.
Entropy pairs for a measure
Authors: Blanchard F. , Host B. , Maass A. , Martinez S. , Rudolph D. J. 
Published: September 2008

AbstractWe define entropy pairs for an invariant measure µ on a topological dynamical system (X, T), and show they allow one to construct the maximal topological factorwith entropy 0 for µ. Then we prove that for any µ, a µ-entropy pair is always topologically so, and the reverse is true when (X, T) is uniquely ergodic.
Classifying C1+ structures on dynamical fractals: 1. The moduli space of solenoid functions for Markov maps on train tracks
Authors: Pinto A. A. , Rand D. A. 
Published: September 2008

AbstractSullivan's scaling function provides a complete description of the smooth conjugacy classes of cookie-cutters. However, for smooth conjugacy classes of Markov maps on a train track, such as expanding circle maps and train track mappings induced by pseudo-Anosov systems, the generalisation of the scaling function suffers from a deficiency. It is difficult to characterise the structure of the set of those scaling functions which correspond to smooth mappings. We introduce a new invariant for Markov maps called the solenoid function. We prove that for any prescribed topological structure, there is a one-to-one correspondence between smooth conjugacy classes of smooth Markov maps and pseudo-Hölder solenoid functions. This gives a characterisation of the moduli space for smooth conjugacy classes of smooth Markov maps. For smooth expanding maps of the circle with degree d this moduli space is the space of Hölder continuous functions on the space {0,…, d − 1}ℕ satisfying the matching condition.
Cohomological rigidity of algebraic ℤd-actions
Authors: Schmidt K. 
Published: September 2008

AbstractWe prove that every Hölder-continuous cocycle for an expansive and mixing ℤd-action α by automorphisms of a compact, abelian group X is Hölder-cohomologous to an affine cocycle, and give a complete description of the Hölder cohomology group of α.
Absolutely continuous invariant measures for piecewise expanding C2 transformations in Rn on domains with cusps on the boundaries
Authors: Adl-Zarabi Kourosh 
Published: September 2008

AbstractLet Ω be a bounded region in Rn and let be a partition of Ω into a finite number of subsets having piecewise C2 boundaries. The boundaries may contain cusps. Let τ: Ω → Ω be piecewise C2 on and expanding in the sense that there exists α > 1 such that for any i = 1, 2,…,m, where is the derivative matrix of and ‖·‖ is the euclidean matrix norm. The main result provides a lower bound on α which guarantees the existence of an absolutely continuous invariant measure for τ.
Nonuniformly hyperbolic K-systems are Bernoulli
Authors: Chernov N. I. , Haskell C. 
Published: September 2008

AbstractWe prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.
Some results on the classification of expansive automorphisms of compact abelian groups
Authors: Fagnani Fabio 
Published: September 2008

AbstractIn this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements isp2for a primep. This yields a classification of the transitive expansive automorphisms with topological entropy logp2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.
Construction of invariant measures supported within the gaps of Aubry–Mather sets
Authors: Forni Giovanni 
Published: September 2008

AbstractThis paper represents a contribution to the variational approach to the understanding of the dynamics of exact area-preserving monotone twist maps of the annulus, currently known as the Aubry–Mather theory. The method introduced by Mather to construct invariant measures of Denjoy type is extended to produce almost-periodic measures, having arbitrary rationally independent frequencies, and positive entropy measures, supported within the gaps of Aubry–Mather sets which do not lie on invariant curves. This extension is based on a generalized version of the Percival's Lagrangian and on a new minimization procedure, which also gives a simplified proof of the basic existence theorem for the Aubry–Mather sets.
On the transfer operator for rational functions on the Riemann sphere
Authors: Denker Manfred , Przytycki Feliks , Urbański Mariusz 
Published: September 2008

AbstractLet T be a rational function of degree ≥ 2 on the Riemann sphere. Our results are based on the lemma that the diameter of a connected component of T−n(B(x, r)), centered at any point x in its Julia set J = J(T), does not exceed Lnrp for some constants L ≥ 1 and ρ > 0. Denote the transfer operator of a Hölder-continuous function φ on J satisfying P(T,φ) > supz∈Jφ(z). We study the behavior of {: n ≥ 1} for Hölder-continuous functions ψ and show that the sequence is (uniformly) normbounded in the space of Hölder-continuous functions for sufficiently small exponent. As a consequence we obtain that the density of the equilibrium measure μ for φ with respect to the -conformal measure is Höolder-continuous. We also prove that the rate of convergence of {ψ to this density in sup-norm is . From this we deduce the corresponding decay of the correlation integral and the central limit theorem for ψ.
θ-transformations, θ-shifts and limit theorems for some Riesz-Raikov sums
Authors: Petit Bernard 
Published: September 2008

AbstractBy Fourier methods, it is possible to prove central limit theorems for Riesz-Raikov sums for any real θ > 1 and for a quite large class of functions f.The same problem is solved here for Hölder-continuous functions f and Pisot–Vijayaragavan numbers θ in a totally different way: it is shown that the question is equivalent to working with ergodic sums for suitable functions F on [0;l], and T denoting the θ-transformation x ↦ θx mod 1. In addition, limit theorems are proved on the θ-shifts, for any real θ 1.
Simple C*-crossed products with a unique trace
Authors: Bédos Erik 
Published: September 2008

AbstractLet (α, u) denote a cocycle-crossed action of a discrete group G on a unital C*-algebra A, and B = C*r (A, G, α, u) the associated reduced (twisted) C*-crossed product. We discuss the following problem: when is B a simple C*-algebra with a unique trace? To this aim, we introduce the concept of tracially properly outerness of actions.
The lap-counting function for linear mod one transformations I: explicit formulas and renormalizability
Authors: Flatto Leopold , Lagarias Jeffrey C. 
Published: September 2008

AbstractLinear mod one transformations are the maps of the unit interval given by fβα(x) = βx + α (mod 1), with β > 1 and 0 ≤ α < 1. The lap-counting function is the function where the lap number Ln essentially counts the number of monotonic pieces of the nth iterate . We derive an explicit factorization formula for Lβα(z) which directly shows that Lβα(z) is a function meromorphic in the open unit disk {z: |z| < 1} and analytic in the open disk {z: |z| < 1/β}, with a simple pole at z = 1/β.Comparison with a known formula for the Artin—Mazur—Ruelle zeta function ζβ,α(z) of fβα shows that Lβα(z) and ζβ,α(z) have identical sets of singularities in the disk {z: |z| < 1}. We derive two more factorization formulae for Lβ,α(z) valid for certain parameter ranges of (β, α). When 1 < α + β ≤ 2, there is sometimes a ‘renormalization’ structure of such maps present, which has previously been studied in connection with simplified models for the Lorenz attractor. In the case that fβα is non-trivially renormalizable, we obtain a factorization formula for Lβα(z). For (β, α) in a region contained in 2 < α + β ≤ 3 we obtain a factorization formula which relates Lβα(z) to a ‘rescaled’ lap-counting function from the region 1 < α + β ≤ 2. The various factorizations exhibit certain singularities of Lβα(z) on the circle |z| = 1/β. These singularities are related to topological dynamical properties of fβ,α. In parts II and III we show that these comprise the complete set of such singularities on the circle |z| = 1/β.
Automorphisms of the Bernoulli endomorphism and a class of skew-products
Authors: Parry William 
Published: September 2008

AbstractWe consider a class of skew-products with base the one-sided two-shift equipped with the (½, ½)Bernoulli measure and fibre either or the circle. We give conditions for the first kind to be isomorphic to the base itself and use this result to establish an isomorphism with the base for the second kind when a certain irrationalis very well approximated by rationals. A consequence is that there is a circle action of automorphisms commuting with theone-sided two-shift.
Non-ergodicity for C1 expanding maps and g-measures
Authors: Quasf Anthony N. 
Published: September 2008

AbstractWe introduce a procedure for finding C1 Lebesgue measure-preserving maps of the circle isomorphic to one-sided shifts equipped with certain invariant probability measures. We use this to construct a C1 expanding map of the circle which preserves Lebesgue measure, but for which Lebesgue measure is non-ergodic (that is there is more than one absolutely continuous invariant measure). This is in contrast with results for C1+e maps. We also show that this example answers in the negative a question of Keane's on uniqueness of g-measures, which in turn is based on a question raised by an incomplete proof of Karlin's dating back to 1953.
Intermingled basins for the triangle map
Authors: Alexander James C. , Hunt Brian R. , Kan Ittai , Yorke James A. 
Published: September 2008

AbstractA family of quadratic maps of the plane has been found numerically for certain parameter values to have three attractors, in a triangular pattern, with ‘intermingled’ basins. This means that for every open set S, if the basin of attraction of one of the attractors intersects S in a set of positive Lebesgue measure, then so do the other two basins. In this paper we mathematically verify this observation for a particular parameter, and prove that our results hold for a set of parameters with positive Lebesgue measure.
Rank and symbolic complexity
Authors: Ferenczi Sébastien 
Published: September 2008

AbstractWe investigate the relation between the complexity function of a sequence, that is the number p(n) of its factors of length n, and the rank of the associated dynamical system, that is the number of Rokhlin towers required to approximate it. We prove that if the rank is one, then lim , but give examples with lim for any prescribed function G with G (n) = 0(an) for every a > 1. We give exact computations for examples of the ‘staircase’ type, which are strongly mixing systems with quadratic complexity. Conversely, for minimal sequences, if p(n) < an + b for some a ≥ 1, the rank is at most 2[a], with bounded strings of spacers, and the system is generated by a finite number of substitutions.