bluuebunny/crossref_metadata_2025_split huggingface dataset:
Entropy of expansive flows
Authors: Thomas Romeo F. 
Published: September 2008

AbstractLet h(φ) be the topological entropy of a real continuous flow φ on a compact metric space X. Introducing an equivalent definition for the topological entropy on an expansive real flow enables us to investigate the topological entropies of mutually conjugate expansive flows and estimate the periodic orbits of an expansive flow which has the pseudo-orbit tracing property.
Dynamics induced on the ends of non-compact manifold
Authors: Alpern Steve , Prasad V. S. 
Published: September 2008

AbstractLet ℋ denote the group of homeomorphisms of a σ-compact manifold M which preserve a locally positive non-atomic measure μ. Such a manifold can be compactified by adjoining ideal points called ‘ends’, collectively denoted by E. Every homeomorphism h in ℋ induces a measure preserving system (E, , μ*, h*) where is the algebra of clopen subsets of E, μ* is a 0-∞ measure induced on E by μ, and h*: E → E is a μ*-preserving homeomorphism. For any induced homeomorphism σ = f*, where f belongs to ℋ, define ℋσ = {h ∈ ℋ: h* = σ}. We prove that ergodicity is generic in ℋσ for the compact-open topology if and only if (E, , μ*, σ) is incompressible and ergodic. Furthermore ℋσ contains an ergodic homeomorphism if and only if (E, , μ*, σ) is incompressible. Since the identity on M induces the identity on E, which is incompressible, our results establish that every manifold (M, μ) supports an ergodic μ-preserving homeomorphism.
The speed interval: a rotation algorithm for endomorphisms of the circle
Authors: Barkmeijer Jan 
Published: September 2008

AbstractLetfbe a continuous map of the circle into itself of degree one. We introduce the notion of rotation algorithms. One of these algorithms associates eachz∈S1with an interval, the so-called speed intervalS(z,f), which is contained in the rotation interval ρ(f) off. In contrast with the rotation set ρ(z,f), the intervalS(z,f) sometimes allows us to ascertain that ρ(f) is non-degenerate, by using only finitely many elements of {fn(z) |n≥ 0}. We further show that all choices for ρ(z,f) andS(z,f) occur, for certainz∈S1provided that ρ(z,f) ⊂S(z,f) ⊂ ρ(f).
An invariant for rigid rank-1 transformations
Authors: Friedman Nathaniel , Gabriel Patrick , King Jonathan 
Published: September 2008

AbstractAssociated to a rigid rank-1 transformationTis a semigroup ℒ(T) of natural numbers, closed under factors. If ℒ(S) ≠ ℒ(T) thenSandTcannot be copied isomorphically onto the same space so that they commute. If ℒ(S) ⊅ ℒ(T) thenScannot be a factor ofT. For each semigroupLwe construct a weak mixingSsuch that ℒ(S) =L. TheSwhere ℒ(S) = {l}, despite having uncountable commutant, has no roots.Preceding and preparing for this example are two others: An uncountable abelian groupGof weak mixing transformations for which any two (non-identity) members have identical self-joinings of all orders and powers. The second example, to contrast with the rank-1 property that the weak essential commutant must be the trivial group, is of a rank-2 transformation with uncountable weak essential commutant.
Duality for automorphisms on a compact C*-dynamical system
Authors: Evans David E. , Kishimoto Akitaka 
Published: September 2008

When considering an action α of a compact group G on a C*-algebra A, the notion of an α-invariant Hilbert space in A has proved extremely useful [1, 4, 8, 14, 17, 18]. Following Roberts [13] a Hilbert space in (a unital algebra) A is a closed subspace H of A such that x*y is a scalar for all x, y in H. For example if G is abelian, and α is ergodic in the sense that the fixed point algebra Aα is trivial, then A is generated as a Banach space by a unitary in each of the spectral subspaceswhich are then invariant one dimensional Hilbert spaces. If G is not abelian, then Hilbert spaces (which are always assumed to be invariant) do not necessarily exist, even for ergodic actions. For non-ergodic actions, it is also desirable to relax the requirement to x*y being a constant multiple of some positive element of Aα. More generally, if γ is a finite dimensional matrix representation of G and n is a positive integer, we define to be the subspacewhere d is the dimension d(γ) of γ, and Mnd denotes n×d complex matrices. (Usually we will denote the extended action of αg to αg ⊗ 1 on A⊗Mnd again by αg.) Let .
Some compact invariant sets for hyperbolic linear automorphisms of torii
Authors: Fathi Albert 
Published: September 2008

AbstractIf the action induced by a pseudo-Anosov map on the first homology group is hyperbolic, it is possible, by a theorem of Franks, to find a compact invariant set for the toral automorphism associated with this action. If the stable and unstable foliations of the Pseudo-Anosov map are orientable, we show that the invariant set is a finite union of topological 2-discs. Using some ideas of Urbański, it is possible to prove that the lower capacity of the associated compact invariant set is >2; in particular, the invariant set is fractal. When the dilatation coefficient is a Pisot number, we can compute the Hausdorff dimension of the compact invariant set.
Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations
Authors: Kanai Masahiko 
Published: September 2008

AbstractWe are concerned with closed C∞ riemannian manifolds of negative curvature whose geodesic flows have C∞ stable and unstable foliations. In particular, we show that the geodesic flow of such a manifold is isomorphic to that of a certain closed riemannian manifold of constant negative curvature if the dimension of the manifold is greater than two and if the sectional curvature lies between − and −1 strictly.
Propriétés des attracteurs de Birkhoff
Authors: Le Calvez P. 
Published: September 2008

AbstractWe study dissipative twist maps of the annulus, following the ideas of G. D. Birkhoff explained in an article of 1932.In the first part, we give complete and rigorous proofs of the results of this article. We define the Birkhoff attractor of a dissipative twist map which has an attracting bounded annulus, we give its main properties and we define its upper and lower rotation numbers.In the second part we give further results on these sets, thus we show that they often coincide with the closure of a hyperbolic periodic point and that they can contain an infinite number of sinks. We also show that the Birkhoff attractors don't depend on a continuous way on the maps.
Rotation intervals for a family of degree one circle maps
Authors: Jonker Leo B. 
Published: September 2008

AbstractLet f be a C0 circle map of degree one with precisely one local minimum and one local maximum, and let [ρ−(f), ρ+(f)] be the interval of rotation numbers of f. We study the structure of the function ρ(λ) = ρ+(Rλ∘f), where Rλ is the rotation through the angle λ.
Realizing symmetries of a shift
Authors: Wagoner J. B. 
Published: September 2008

AbstractAll subshifts of finite type are known to appear as basic parts of the non-wandering sets of Smale diffeomorphisms in dimensions three or more. This paper concerns the symmetries of subshifts of finite type; that is, the homeomorphisms of the shift space which commute with the shift. The group of symmetries is known to be very large for aperiodic shifts. For certain (structually stable) Smale diffeomorphisms of the sphere of dimension five or more, we show each symmetry can be extended to a homeomorphism of the sphere commuting with the diffeomorphism on the whole sphere.
Infinite limits in the iteration of entire functions
Authors: Baker I. N. 
Published: September 2008

AbstractIf f is a transcendental entire function and D is a non-wandering component of the set of normality of the iterates of f such that fn → ∞ in D then log |fn(z)| = O(n) as n → ∞ for z in D. For a wandering component the convergence of fn to ∞ in D may be arbitrarily fast.
Rotation shadowing properties of circle and annulus maps
Authors: Barge Marcy , Swanson Richard 
Published: September 2008

AbstractWe define the notions of the pseudo-rotation set and rotation shadowing of pseudo-orbits for endomorphisms of the circle and for homeomorphisms of the annulus. The results include: the rotation shadowing property holds for all endomorphisms of the circle; the pseudo-rotation set equals the closure of the rotation set; the closure of the rotation set varies upper-semicontinuously.
Regular dependence of invariant curves and Aubry–Mather sets of twist maps of an annulus
Authors: Douady Raphaël 
Published: September 2008

AbstractWe prove that smooth enough invariant curves of monotone twist maps of an annulus with fixed diophantine rotation number depend on the map in a differentiable way. Partial results hold for Aubry-Mather sets.Then we show that invariant curves of the same map with different rotation numbers ω and ω′ cannot approach each other at a distance less than cst. |ω−ω′|. By K.A.M. theory, this implies that, under suitable assumptions, the union of invariant curves has positive measure.Analogous results are due to Zehnder and Herman (for the first part), and to Lazutkin and Pöschel (for the second one), in the case of Hamiltonian systems and area preserving maps.
Dynamics of the geodesic flow of a foliation
Authors: Walczak Paweł G. 
Published: September 2008

AbstractThe geodesic flow of a foliated Riemannian manifold (M, F) is studied. The invariance of some smooth measure is established under some geometrical conditions on F. The Lyapunov exponents and the entropy of this flow are estimated. As an application, the non-existence of foliations with ‘short’ second fundamental tensors is obtained on compact negatively curved manifolds.
Generalized baker's transformations
Authors: Bose Christopher J. 
Published: September 2008

AbstractA class of automorphisms of the unit square called generalized baker'stransformations (gbt) is defined in such a way that every stationary stochastic process may be represented as the movement of a simple partition of the square under a gbt. This extends the classical example of the representation of independent processes by the well-known baker's transformation.Every ergodic, positive-entropy automorphism is measurably isomorphic to some gbt (again generalizing the classical result about Bernoulli shifts), and we show that a large class of gbt's satisfying certain continuity restrictions are actually measurably isomorphic to Bernoulli shifts.
Un exemple de transformation dilatante et C1 par morceaux de l'intervalle, sans probabilité absolument continue invariante
Authors: Gora P. , Schmitt B. 
Published: September 2008

AbstractWe construct a transformation on the interval [0, 1] into itself, piecewiseC1 and expansive, which doesn't admit any absolutely continuous invariant probability measure (a.c.i.p.).So in this case we give a negative answer to a question by Anosov: is C1 character sufficient for the existence of absolutely continuous measure?Moreover, in our example,ƒ' has a modulus of type K/(|1+|log|x‖); it is known that a modulus of continuity of type K/(1+|log|x‖)1+γ, γ>0 implies the existence of a.c.i.p..
On ergodic properties of restrictions of inner functions
Authors: Martin N.F.G. 
Published: September 2008

AbstractWe consider inner functions on the unit disk which have a finite number of singularities on the unit circle. The restriction of such functions to the circle are maps onto the circle. We give sufficient conditions that these restrictions are exact endomorphisms whose natural extensions are Bernoulli and that the entropy is given by Rohlin's formula, We also give the entropy in closed form if ƒ' is in the Nevalinna class N. An example is considered. In the last section we show that if two restrictions are metrically isomorphic, they are diffeomorphic.
Compact metric spaces, Fredholm modules, and hyperfiniteness
Authors: Connes A. 
Published: September 2008

AbstractWe show that the existence of a finitely summable unbounded Fredholm module (h, D) on a C* algebra A implies the existence of a trace state on A and that no such module exists on the C* algebra of a non amenable discrete group. Both for the needs of non commutative differential geometry and of analysis in infinite dimension we are led to the better notion of the θ-summable Fredholm module.
Topology and growth of a special class of holomorphic self-maps of ℂ*
Authors: Keen Linda 
Published: September 2008

AbstractIt is a general problem to find appropriate sets of moduli for families of functions that generate dynamical systems. In this paper we solve this problem for a specific family of holomorphic self-maps of ℂ* defined byThe main theorem states that any function topologically conjugate to a member of ℱ is holomorphically conjugate to some member of the family. It follows that the coefficients of the polynomials P(z) and Q(z) are a suitable set of moduli for the families of dynamical systems generated by these functions.The moduli spaces of functions in ℱ are easy to study computationally and have been studied by many authors. (See references in the text.)
The conjugacy of Collet–Eckmann's map of the interval with the tent map is Holder continuous
Authors: Nowicki T. , Przytycki F. 
Published: September 2008

AbstractIt is proved that a homeomorphism h, which conjugates a smooth unimodal map of the interval with negative Schwarzian derivative and positive Lyapunov exponent along the forward trajectory of the critical value with a tent map, and its inverse h−1 are Hölder continuous.
Discontinuity of Hausdorff dimension and limit capacity on arcs of diffeomorphisms
Authors: Diaz Lorenzo J. , Viana Marcelo 
Published: September 2008

AbstractWe consider one-parameter families of torus diffeomorphisms that bifurcate from global hyperbolic maps (Anosov) to DA maps (derived from Anosov). For an open set of these families, we show that the Hausdorff dimension and limit capacity of the nonwandering set are not continuous across the bifurcation. We also study the behaviour of equilibrium measures near the bifurcation.
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows
Authors: Feres Renato , Katok Anatoly 
Published: September 2008

AbstractWe consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
Authors: Guivarc'h Y. 
Published: September 2008

AbstractWe study the ergodic properties of a class of dynamical systems with infinite invariant measure. This class contains skew-products of Anosov systems with ℝd. The results are applied to theKproperty of skew-products and also to the ergodicity of the geodesic flow on abelian coverings of compact manifolds with constant negative curvature.
A new description of the Bowen—Margulis measure
Authors: Hamenstädt Ursula 
Published: September 2008

AbstractThe Bowen-Margulis measure on the unit tangent bundle of the universal covering of a compact manifold of negative curvature is determined by its restriction to the leaves of the strong unstable foliation. We describe this restriction to any strong unstable manifold W as a spherical measure with respect to a natural distance on W.
Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems: 1. The case of negative Schwarzian derivative
Authors: Lyubich M. Yu. 
Published: September 2008

AbstractIt is proved that an arbitrary one dimensional dynamical system with negative Schwarzian derivative and non-degenerate critical points has no wandering intervals. This result implies a rather complete view of the dynamics of such a system. In particular, every minimal topological attractor is either a limit cycle, or a one dimensional manifold with boundary, or a solenoid. The orbit of a generic point tends to some minimal attractor.
Minimal self-joinings for nonsingular transformations
Authors: Rudolph Daniel J. , Silva Cesar E. 
Published: September 2008

AbstractThe notion of minimal self-joinings for conservative nonsingular actions is defined as a restriction on the nature of rational self-joinings. The need to consider rational joinings is demonstrated by showing that any two type II1actions whose Cartesian product is ergodic have type IIIλnonsingular joinings. Lastly, actions of all Krieger types with minimal self-joinings are constructed. Hence these actions are prime and commute only with their powers.
Monotone recurrence relations, their Birkhoff orbits and topological entropy
Authors: Angenent Sigurd B. 
Published: September 2008

AbstractA generalization of the class of monotone twistmaps to maps ofs1×RNis proposed. The existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given. These results are then specialized to the case of monotone twist maps. Finally it is shown that there is a large class of symplectic maps to which the foregoing discussion applies.
Regular isomorphism of Markov chains is almost topological
Authors: Boyle Mike , Tuncel Selim 
Published: September 2008

AbstractTwo Markov chains are regularly isomorphic if and only if they have a common Markov extension by right closing block codes of degree one. A certain ideal class in the integral group ring of the ratio group associated to a Markov chain is a new invariant of regular isomorphism and some other coding relations.
Stability of m-equivalence to the weak Pinsker property
Authors: Fieldsteel Adam , Rudolph Daniel J. 
Published: September 2008

AbstractLet denote the class of transformations with the weak Pinsker property, and let []m denote the class of transformations m-equivalent to some member of , where m is an entropy-preserving size. We show that if T is a factor of an element of []m, then T ∈ []m, and if T is an m-limit of elements of []m, then T ∈ []m.
The growth rate of trajectories of a quadratic differential
Authors: Masur Howard 
Published: September 2008

AbstractSupposeqis a holomorphic quadratic differential on a compact Riemann surface of genusg≥ 2. Thenqdefines a metric, flat except at the zeroes. A saddle connection is a geodesic joining two zeroes with no zeroes in its interior. This paper shows the asymptotic growth rate of the number of saddles of length at mostTis at most quadratic inT. An application is given to billiards.
On the topological stable rank of certain transformation group C*-algebras
Authors: Putnam Ian F. 
Published: September 2008

AbstractWe consider the crossed product or transformation group C*-algebras arising from actions of the group of integers on a totally disconnected compact metrizable space. Under a mild hypothesis, we give a necessary and sufficient dynamical condition for the invertibles in such a C*-algebra to be dense. We also examine the property of residual finiteness for such C*-algebras.
Parabolic fixed points, invariant curves and action-angle variables
Authors: Aharonov Dov , Elias Uri 
Published: September 2008

AbstractA fixed point of an area-preserving mapping of the plane is called elliptic if the eigenvalues of its linearization are of unit modulus but not ±1; it is parabolic if both eigenvalues are 1 or −1. The elliptic case is well understood by Moser's theory. Here we study when is a parabolic fixed point surrounded by closed invariant curves. We approximate our mapping T by the phase flow of an Hamiltonian system. A pair of variables, closely related to the action-angle variables, is used to reduce T into a twist mapping. The conditions for T to have closed invariant curves are stated in terms of the Hamiltonian.
Minimal geodesics
Authors: Bangert Victor 
Published: September 2008

AbstractMotivated by the close relation between Aubry-Mather theory and minimal geodesies on a 2-torus we study the existence and properties of minimal geodesics in compact Riemannian manifolds of dimension ≥3. We prove that there exist minimal geodesics with certain rotation vectors and that there are restrictions on the rotation vectors of arbitrary minimal geodesics. A detailed analysis of the minimal geodesics of the ‘Hedlund examples’ shows that – to a certain extent – our results are optimal.
Invariant manifolds for near identity differentiable maps and splitting of separatrices
Authors: Fontich E. , Simó C. 
Published: September 2008

AbstractWe consider families of differentiable diffeomorphisms with hyperbolic points, close to the identity, which tend to it when the parameter goes to zero.We study the asymptotic behaviour of the invariant manifolds. Then we consider the case when there are homo-heteroclinic points and we find that the maximum separation between the invariant manifolds is of the order of some power of the parameter which is related to the degree of differentiability.Finally the analogous case for flows is considered.
×2 and ×3 invariant measures and entropy
Authors: Rudolph Daniel J. 
Published: September 2008

AbstractLet p and q be relatively prime natural numbers. Define T0 and S0 to be multiplication by p and q (mod 1) respectively, endomorphisms of [0,1).Let μ be a borel measure invariant for both T0 and S0 and ergodic for the semigroup they generate. We show that if μ is not Lebesgue measure, then with respect to μ both T0 and S0 have entropy zero. Equivalently, both T0 and S0 are μ-almost surely invertible.
Connecting ergodicity and dimension in dynamical systems
Authors: Cutler C. D. 
Published: September 2008

AbstractIn this paper we make precise the relationship between local or pointwise dimension and the dimension structure of Borel probability measures on metric spaces. Sufficient conditions for exact-dimensionality of the stationary ergodic distributions associated with a dynamical system are obtained. A counterexample is provided to show that ergodicity alone is not sufficient to guarantee exactdimensionality even in the case of continuous maps or flows.
A topological version of a theorem of Veech and almost simple flows
Authors: Glasner Eli 
Published: September 2008

AbstractAlmost simple (AS) minimal flows are defined and it is shown that any factor map of an AS flow is, up to almost 1−1 equivalence, a group factor. An analogous theorem for metric, regular, point distal extensions is proved. In particular a theorem of Gottschalk is strengthened to show that any regular, point distal, metric flow is equicontinuous. When the acting groupTis commutative it is shown that every proper minimal joining of an AS flowXand a minimal flowY, is, up to almost 1−1 extensions, the relative product ofXandYover a common factor which is a group factor ofX.
Un théorème de disjonction de systèmes dynamiques et une généralisation du théorème ergodique de Wiener—Wintner
Authors: Lesigne E. 
Published: September 2008

AbstractIf (Ω, μ, T) is a measure preserving system and if ƒ ∈ L1(μ) then, for almost all ω, for every real polynomial P, the sequenceTo prove this result we use the concept of disjointness of dynamical systems and the fact that disjointness is preserved by isometric extensions.
The number of limit cycles of polynomial deformations of a Hamiltonian vector field
Authors: Mardešić P. 
Published: September 2008

AbstractWe prove that the lowest upper bound for the number of limit cycles of small nonconservative polynomial deformations of degree n of the Hamiltonian vector field is n − 1.A consequence is that the lowest upper bound for the number of limit cycles of generic n-parameter deformations of cusps is n − 1.
On Cherry flows
Authors: Martens Marco , Strien Sebastian Van , Melo Welington De , Mendes Pedro 
Published: September 2008

AbstractThe purpose of this research is to describe all smooth vector fields on the torus T2 with a finite number of singularities, no periodic orbits and no saddleconnections. In this paper we are able to complete the description within the class of vector fields which are area contracting near all singularities. In particular we give a large class of analytic vector fields on the torus T2 which have non-trivial recurrence and also sinks.