bluuebunny/crossref_metadata_2025_split huggingface dataset:
Maximal absolutely continuous invariant measures for piecewise linear Markov transformations
Authors: Byers W. , Góra P. , Boyarsky A. 
Published: September 2008

AbstractLet be an irreducible 0–1 matrix such that the non-zero entries in each row are consecutive. Let be the class of piecewise linear Markov transformations τ on [0, 1] into [0, 1] induced by for which the absolutely continuous invariant measure has maximal entropy. The main result presents necessary and sufficient slope conditions on τ which guarantee that τ ∈ .
Ergodic aspects of cellular automata
Authors: Hurley Mike 
Published: September 2008

AbstractThis paper contains a study of attractors in cellular automata, particularly the minimal attractors as defined by J. Milnor. Milnor's definition of attractor uses a measure on the state space; the measures that we consider are Bernoulli product measures. Given a Bernoulli measure it is shown that a cellular automaton has at most one minimal attractor; when there is one, it is the omega-limit set of almost all points. Examples are given to show that the minimal attractor can change as the Bernoulli measure is varied. Other examples illustrate the difference between this result and the corresponding result that is obtained by replacing Milnor's definition of attractor by the purely topological definition used by C. Conley. The examples also show that certain invariant sets of cellular automata are less well-behaved than one might hope: for instance the periodic points are not necessarily dense in the nonwandering set.
Eventual factor maps and compositions of closing maps
Authors: Kitchens Bruce , Marcus Brian , Trow Paul 
Published: September 2008

AbstractWe prove some results related to the question of the existence of factor maps and eventual factor maps between shifts of finite type. Our main result is that if A and B are integral eventually positive (IEP) matrices, and A eventually factors finite-to-one onto B, then there exists an IEP matrix C such that A eventually factors onto C by left closing maps and C eventually factors onto B by right closing maps. This answers the question of the existence of finite-to-one eventual factor maps when the spectrum of A is simple. As a corollary, if in addition to the above hypothesis, χ*A=χ*B, (where χ*A is the characteristic polynomial of A modulo x), then A is shift equivalent to B.
Rotation vectors and entropy for homeomorphisms of the torus isotopic to the identity
Authors: Llibre J. , Mackay R. S. 
Published: September 2008

AbstractWe show that if a homeomorphism f of the torus, isotopic to the identity, has three or more periodic orbits with non-collinear rotation vectors, then it has positive topological entropy. Furthermore, for each point ρ of the convex hull Δ of their rotation vectors, there is an orbit of rotation vector ρ, for each rational point p/q, p ∈ ℤ2, q ∈ ℕ, in the interior of Δ, there is a periodic orbit of rotation vector p / q, and for every compact connected subset C of Δ there is an orbit whose rotation set is C. Finally, we prove that f has ‘toroidal chaos’.
Systems of differential equations that are competitive or cooperative. VI: A localCrClosing Lemma for 3-dimensional systems
Authors: Hirsch Morris W. 
Published: September 2008

AbstractFor certainCr3-dimensional cooperative or competitive vector fieldsF, whereris any positive integer, it is shown that for any nonwandering pointp, every neighborhood ofFin theCrtopology contains a vector field for whichpis periodic, and which agrees withFoutside a given neighborhood ofp. The proof is based on the existence of invariant planar surfaces throughp.
Stability of Lyapunov exponents
Authors: Ledrappier F. , Young L.-S. 
Published: September 2008

AbstractWe consider small random perturbations of matrix cocycles over Lipschitz homeomorphisms of compact metric spaces. Lyapunov exponents are shown to be stable provided that our perturbations satisfy certain regularity conditions. These results are applicable to dynamical systems, particularly to volume-preserving diffeomorphisms.
-Convergence to equilibrium and space—time bernoullicity for spin systems in the M < ε case
Authors: Steif Jeffrey E. 
Published: September 2008

AbstractLiggett has proved that for spin systems, Markov processes with state space {0,1}ℤn, there is a unique stationary distribution in the M < ε regime and all initial configurations uniformly approach this unique stationary distribution exponentially in the weak topology. Here, M and ε are two parameters of the system. We extend this result to discrete time but strengthen it by proving exponential convergence in the stronger - metric instead of the usual weak topology. This is then used to show that the unique stationary process with state space {0,1}ℤn and index set ℤ is isomorphic (in the sense of ergodic theory) to an independent process indexed by ℤ. In the translation invariant case, we prove the stronger fact that this stationary process viewed as a {0, l}-valued process with index set ℤn × ℤ (spacetime) is isomorphic to an independent process also indexed by ℤn × ℤ. This shows that this process is in some sense the most random possible. An application of this last result to approximating by an infinite number of finite systems concatenated independently together is also presented. Finally, we extend all of these results to continuous time.
Iterates of meromorphic functions III: Preperiodic domains
Authors: Baker I. N. , Kotus J. , Yinian Lü 
Published: September 2008

AbstractThe paper discusses the connectivity of periodic and preperiodic domains in the stable set in the iteration of a meromorphic function. The connectivity of an invariant component has one of the values 1, 2, ∞. Examples are constructed to show that the connectivity of a preperiodic component may take any value.
Rotation and periodicity in plane separating continua
Authors: Barge Marcy , Gillette Richard M. 
Published: September 2008

AbstractWe prove that ifFis an orientation-preserving homeomorphism of the plane that leaves invariant a continuum Λ which irreducibly separates the plane into exactly two domains, then the convex hull of the rotation set ofFrestricted to Λ is a closed interval and each reduced rational in this interval is the rotation number of a periodic orbit in Λ. We also show that the interior and exterior rotation numbers ofFassociated with Λ are contained in the convex hull of the rotation set ofFrestricted to Λ and that if this set is nondegenerate then Λ is an indecomposable continuum.
Geodesic flows on manifolds of negative curvature with smooth horospheric foliations
Authors: Feres Renato 
Published: September 2008

AbstractWe improve and extend a result due to M. Kanai about rigidity of geodesic flows on closed Riemannian manifolds of negative curvature whose stable or unstable horospheric foliation is smooth. More precisely, the main results proved here are: (1) Let M be a closed C∞ Riemannian manifold of negative sectional curvature. Assume the stable or unstable foliation of the geodesic flow φt: V → V on the unit tangent bundle V of M is C∞. Assume, moreover, that either (a) the sectional curvature of M satisfies −4 < K ≤ −1 or (b) the dimension of M is odd. Then the geodesic flow of M is C∞-isomorphic (i.e., conjugate under a C∞ diffeomorphism between the unit tangent bundles) to the geodesic flow on a closed Riemannian manifold of constant negative curvature. (2) For M as above, assume instead of (a) or (b) that dim M ≡ 2(mod 4). Then either the above conclusion holds or φ1, is C∞-isomorphic to the flow , on the quotient Γ\, where Γ is a subgroup of a real Lie group ⊂ Diffeo () with Lie algebra is the geodesic flow on the unit tangent bundle of the complex hyperbolic space ℂHm, m = ½ dim M.
Spectral properties of a class of operators associated with maps in one dimension
Authors: Ruelle David 
Published: September 2008

AbstractLet f be a piecewise monotone map of the interval [0,1] to itself, and g a function of bounded variation on [0, 1]. Hofbauer, Keller and Rychlik have studied operators on functions of bounded variation, whereAmong other things, they show that the essential spectral radius of is in many cases strictly smaller than the spectral radius; there exist therefore isolated eigenvalues of finite multiplicity. The purpose of the present paper is to prove similar results for a more general class of operators forming an algebra (and therefore containing sums of operators like ). An analogous extension was presented by Ruelle for operators associated with expanding maps.
Random sets for the pointwise ergodic theorem
Authors: Huang Yenkun 
Published: September 2008

AbstractWe generalize a result of Bourgain and devise more general criteria which guarantee that the corresponding random set in Z+ almost surely satisfies a pointwise ergodic theorem on Lp for p > 1. Several large classes of examples are constructed. We also show that under a simple condition the corresponding random set in Z+ almost surely satisfies a pointwise ergodic theorem not only on Lp for p > 1 but also on L1. On the other hand, we establish a criterion to conclude that a certain class of random sets have Banach density zero. In particular, all of the examples mentioned have Banach density zero.
Dynamical properties of the shift maps on the inverse limit spaces
Authors: Li Shihai 
Published: September 2008

AbstractIn this paper, we prove the following results about the shift map on the inverse limit space of a compact metric space and a sole bonding map: (1) the chain recurrent set of the shift map equals the inverse limit space of the chain recurrent set of the sole bonding map. Similar results are proved for the nonwandering set, ω-limit set, recurrent set, and almost periodic set. (2) The shift map on the inverse limit space is chaotic in the sense of Devaney if and only if its sole bonding map is chaotic. (3) If the sole bonding map is ω-chaotic, then the shift map on the inverse limit space is ω-chaotic. With a modification of the definition of ω-chaos we show the converse is true. (4) We prove that a transitive map on a closed invariant set containing an interval must have sensitive dependence on initial conditions on the whole set. Then it is both ω-chaotic and chaotic in the sense of Devaney with chaotic set the whole set. At last we give a new method of constructing chaotic homeomorphisms on chainable continua, especially on pseudo-arcs.
The Bernoulli property of inner functions
Authors: Craizer Marcos 
Published: September 2008

AbstractLet f: D → D be an inner function with a fixed point p ∈ D, and f*: S1 → S1 be its extension to the unit circle. We prove in this paper that the Rohlin invertible extension of the system (f*, λp) is equivalent to a generalized Bernoulli shift, where λp is the harmonic measure associated with p.
A classification of the isometric extensions of a multidimensional Bernoulli shift
Authors: Kammeyer Janet Whalen 
Published: September 2008

AbstractThe isometric extensions of a multidimensional Bernouli shift are classified completely, up to C-isomorphism, and up to isomorphism. If such an extension is weakly mixing then it must be Bernoulli; otherwise, it has a rotation factor, which has a Bernoulli complementary algebra. This result is extended to multidimensional Bernoulli flows and Bernoulli shifts of infinite entropy.
Countable sections for locally compact group actions
Authors: Kechris Alexander S. 
Published: September 2008

AbstractIt has been shown by J. Feldman, P. Hahn and C. C. Moore that every non-singular action of a second countable locally compact group has a countable (in fact so-called lacunary) complete measurable section. This is extended here to the purely Borel theoretic category, consisting of a Borel action of such a group on an analytic Borel space (without any measure). Characterizations of when an arbitrary Borel equivalence relation admits a countable complete Borel section are also established.
Rotation number and one-parameter families of circle diffeomorphisms
Authors: Tsujii Masato 
Published: September 2008

AbstractWe consider one-parameter families of circle diffeomorphisms, f1(x) = f(x) + t(t ∈ S1), where f: S1 is a Cr-diffeomorphism (r≥3). We show that, for Lebesgue almost every t ∈ S1 the rotation number of f1, is either a rational number or an irrational number of Roth type. In the former case, f1, has periodic orbits and, in the latter case, f1, is Cr − 2-conjugate to an irrational rigid rotation from well-known theorems of Herman and Yoccoz.
A new maximal inequality and its applications
Authors: Rosenblatt Joseph M. , Wierdl Mate 
Published: September 2008

AbstractThere is a maximal inequality on the integers which implies not only the classical ergodic maximal inequality and certain maximal inequalities for moving averages and differentiation theory, but it also has the following consequence: let P1 ≤ P2 ≤ … ≤ Pk+1 be positive integers. For a σ-finite measure-preserving system (Ω, β, μ, T) and an a.e. finite β-measurable f denoteThen for any λ > 0 and f ∈ L1(Ω)We show how the multi-parametric and superadditive versions of the previous equation can be obtained from the corresponding inequality for reversed supermartingales. The possibility of similar theorems for martingales and other sequences is also discussed.
Dynamics of periodically forced parabolic equations on the circle
Authors: Sandstede Björn , Fiedler Bernold 
Published: September 2008

AbstractWe consider the dynamics of scalar reaction-diffusion equations:We show that every prescribed vectorfield in the plane embeds into equation (1) for a suitable f = f (t, x, u, ux). In contrast, suppose f = f (t, u, ux) is independent of x and T-periodic in t. Then the ω-limit set of any bounded solution is a subset of some two-dimensional torus carrying a linear flow.
Følner Independence and the amenable Ising model
Authors: Adams Scot 
Published: September 2008

AbstractWe define a criterion called Følner Independence for a stationary process over an amenable group. Intuitively, a process satisfies the criterion if, for sufficiently invariant Følner sets, the process in the Følner set is nearly independent of the process outside. We show that Følner Independence implies Finitely Determined. As an application, we show that, in its extreme Gibbs states, the amenable attractive Ising model is Følner Independent (hence Finitely Determined, hence Bernoulli).
An area preserving homeomorphism of T2 that is fixed point free but does not move any essential simple closed curve off itself
Authors: Bestvina Mladen , Handel Michael 
Published: September 2008

AbstractWe construct an area preserving homeomorphism ƒ: T2→T2 that is isotopic to the identity and fixed point free, but has the property that every essential simple closed curve C satisfies ƒ(C)∩C ≠ Ø. This answers a question of Guillou.
The equivalence theorem for ℤd-actions of positive entropy
Authors: Hasfura-Buenaga J. Roberto 
Published: September 2008

AbstractFirst, the class of id-finitely fixed actions of ℤdon a Lebesgue space is defined. Then, it is demonstrated that this property is stable under id-Kakutani equivalence and that, conversely, any two id-finitely fixed ℤd-actions of the same (finite) positive entropy are id-Kakutani equivalent. By id-Kakutani equivalence we mean that element in A. del Junco and D. Rudolph's family of relations on ℤd-actions corresponding to the identityd×dmatrix.
On the classification of some two-dimensional Markov shifts with group structure
Authors: Shereshevsky Mark A. 
Published: September 2008

AbstractFor a finite Abelian group G define the two-dimensional Markov shift for all . Let μG be the Haar measure on the subgroup . The group ℤ2 acts on the measure space (XG, MG) by shifts. We prove that if G1, and G2 are p-groups and E(G1,) ≠ E(G2), where E(G) is the least common multiple of the orders of the elements of G, then the shift actions on and are not measure-theoretically isomorphic. For any finite Abelian groups G1 and G2 the shift actions on and are topologically conjugate if and only if G1 and G2 are isomorphic.
A characterization of ω-limit sets of maps of the interval with zero topological entropy
Authors: Bruckner A. M. , Smítal J. 
Published: September 2008

AbstractWe prove that an infiniteW⊂ (0, 1) is an ω-limit set for a continuous map ƒ of [0,1] with zero topological entropy iffW=Q∪PwhereQis a Cantor set, andPis countable, disjoint fromQ, dense inWif non-empty, and such that for any intervalJcontiguous toQ, card (J∩P) ≤ 1 if 0 or 1 is inJ, and card (J∩P) ≤ 2 otherwise. Moreover, we prove a conjecture by A. N. Šarkovskii from 1967 thatPcan contain points from infinitely many orbits, and consequently, that the system of ω-limit sets containingQand contained inW, can be uncountable.
Regularity of time-preserving conjugacies for contact Anosov flows withC1-Anosov splitting
Authors: Hamenstädt Ursula 
Published: September 2008

AbstractLet(resp.) be a smooth contact flow on a compact manifoldV1(resp.)V2with Anosov splitting of classC1. We show that every time-preserving conjugacy Λ:(V1,)→(V2,) is necessarily of classC2.
Uniformly quasi-isometric foliations
Authors: Kellum Mark 
Published: September 2008

AbstractConsider the natural action of 1-jets of the holonomy pseudogroup H on the transverse tangent bundle of a C1 compact foliated manifold (M, ℱ). If these 1-jets act in an equicontinuous way then it is possible to use a C1 ‘Ellis semi-group’ technique, as applied to a neighborhood of the identity in H, to produce a sheaf of compact local transformation groups whose orbits are the topological closures of leaves of ℱ. This action on the transverse manifold to ℱ then decomposes M into a union of minimal sets. These minimal sets we show to be C1 embedded submanifolds of M and the action of H on them is locally transitive.
Algebraic torsion, zeta function and Dirichlet series for graph links in homology 3-spheres
Authors: Némethi András 
Published: September 2008

AbstractIn this paper, we define the algebraic torsion τ associated with an -constructible sheaf ℱ on a topological space X and a ring homomorphism π1(X) → Z (with an acyclicity condition). If (X, ) has a fiber structure over S1, then τ is equal to the zeta function of the monodromy acting on the hypercohomology of the fiber. If X is the complement of a link in a homology 3-sphere and is given by a link such that admits a fiberable splice diagram, then this zeta function has a product decomposition (corresponding to the Jaco-Shalen-Johansson decomposition). This can be interpreted as a ‘Lefschetz type formula’ for a dynamical system suitably chosen.
Multiplicity two actions and loop space homology
Authors: Paternain Gabriel P. 
Published: September 2008

AbstractWe study Hamiltonian actions of compact Lie groups with low dimensional Marsden-Weinstein reduced spaces. We show that Hamiltonian systems with such symmetry groups have zero topological entropy and easily described dynamics. As a result we show that if the geodesic flow of a compact simply connected Riemannian manifold admits such a symmetry group, then the loop space homology of the manifold grows sub-exponentially with any field coefficient. Topological obstructions for collective complete integrability are thus obtained.
Core dimension group constraints for factors of sofic shifts
Authors: Trow Paul , Williams Susan 
Published: September 2008

AbstractWe give constraints on the existence of factor maps between sofic shifts. These constraints yield examples of sofic shifts of entropy lognwhich do not factor onto the fulln-shift. We also show that any prime which divides the degree of an endomorphism of a sofic shift must divide the non-leading coefficients of the characteristic polynomial of the core matrix of the shift.
On the asymptotic range of cocyles for shifts of finite type
Authors: Coelho Zaqueu 
Published: September 2008

AbstractWe study the problem of lifting ergodicity to certain skew-product extensions over shifts of finite type. This can be done by computing the asymptotic range of the defining cocycle. For a class of ergodic shift-invariant measures and a class of functions (defining conservative extensions) we give a characterization of ergodicity in terms of weights of periodic orbits in the shift space.
Closed orbits in homology classes for Anosov flows
Authors: Sharp Richard 
Published: September 2008

AbstractWe consider transitive Anosov flows φ:M→Mand give necessary and sufficient conditions for every homology class inH1(M,ℤ) to contain a closed φ-orbit. Under these conditions, we derive an asymptotic formula for the number of closed φ-orbits in a fixed homology class, generalizing a result of Katsuda and Sunada.
A stochastic analogue of a theorem of Boyle's on almost flow equivalence
Authors: Araújo Paulo Ventura 
Published: September 2008

AbstractWe study a new topological classification of suspension flows on subshifts of finite type, and obtain a new proof of a theorem of Boyle's which states that, in an appropriate sense, all such flows are alike. We prove that the stochastic version of this classification is non-trivial by exhibiting a certain invariant, and show that this invariant is complete in a particular case, although not in general. Symbolic flows are important as models of basic sets of Axiom A flows, and so we discuss the significance of our results for this latter type of flow.
Crossed products of totally disconnected spaces by
Authors: Bratteli Ola , Evans David E. , Kishimoto Akitaka 
Published: September 2008

AbstractLet Ω be a totally disconnected compact metrizable space, and let α be a minimal homeomorphism of Ω. Let σ be a homeomorphism of order 2 on Ω such that ασ = σα−1, and assume that σ or ασ has a fixed point. We prove (Theorem 3.5) that the crossed productis an AF-algebra.
Gradient-like flows on 3-manifolds
Authors: de Rezende K. A. 
Published: September 2008

AbstractIn this paper, we determine properties that a Lyapunov graph must satisfy for it to be associated with a gradient-like flow on a closed orientable three-manifold. We also address the question of the realization of abstract Lyapunov graphs as gradient-like flows on three-manifolds and as a byproduct we prove a partial converse to the theorem which states the Morse inequalities for closed orientable three-manifolds. We also present cancellation theorems of non-degenerate critical points for flows which arise as realizations of canonical abstract Lyapunov graphs.
α-equivalence: a refinement of Kakutani equivalence
Authors: Fieldsteel Adam , Del Junco Andrés , Rudolph Daniel J. 
Published: September 2008

AbstractFor a fixed irrational α > 0 we say that probability measure-preserving transformationsSandTare α-equivalent if they can be realized as cross-sections in a common flow such that the return time functions on the cross-sections both take values in {1, 1 +α} and have equal integrals. Similarly we call two flowsFandGα-equivalent ifFhas a cross-sectionSandGhas a cross-sectionTisomorphic toSand again both the return time functions take values in {1, 1 + α} and have equal integrals. The integer kα(S), equal to the least positivesuchsuch that exp2πikα-1belongs to the point spectrum ofS, is an invariant of α-equivalence.We obtain a characterization of a-equivalence as a particular type of restricted orbit equivalence and use this to prove that within the class of loosely Bernoulli mapska(S) together with the entropyh(S) are complete invariants of α-equivalence. There is a corresponding a-equivalence theorem for flows which has as a consequence, for example, that up to an obvious entropy restriction, any weakly mixing cross-section of a loosely Bernoulli flow can also be realized as a cross-section with a {1,1 + α}-valued return time function.For the proof of the α-equivalence theorem we develop a relative Kakutani equivalence theorem for compact group extensions which is of interest in its own right. Finally, an example of Fieldsteel and Rudolph is used to show that in generalkα(S) is not a complete invariant of α-equivalence within a given even Kakutani equivalence class.