bluuebunny/crossref_metadata_2025_split huggingface dataset:
A local limit theorem for a sequence of interval transformations
Authors: Calderoni P. , Campanino M. , Capocaccia D. 
Published: September 2008

AbstractLet λ > 1 be a real eigenvalue of an automorphism of the two dimensional torus. We prove that for a dense, open subset of intervals the sequence where {x} denotes the fractional part of x and χ[a, b] the characteristic function of [a, b], satisfies the local limit theorem with respect to Lebesgue measure on [0, 1].
Simplicial systems for interval exchange maps and measured foliations
Authors: Kerckhoff S. P. 
Published: September 2008

AbstractThe spaces of interval exchange maps and measured foliations are considered and an alternative proof that almost all interval exchange maps and measured foliations are uniquely ergodic is given. These spaces are endowed with a refinement process, called a simplicial system, which is studied abstractly and is shown to be normal under a simple assumption. The results follow and thus are a corollary of a more general theorem in a broader setting.
The entropy of C2 surface diffeomorphisms in terms of Hausdorff dimension and a Lyapunov exponent
Authors: Mendoza Leonardo 
Published: September 2008

AbstractIn this paper we prove that if the entropy of an ergodic measure preserved by a C2 surface diffeomorphism is positive then it is equal to the product of the Hausdorff dimension of the quotient measure defined by the family of stable manifolds and the positive Lyapunov exponent.
Errata to ‘Hausdorff dimension for horseshoes’
Authors: Manning Anthony 
Published: September 2008

In our paper ‘Hausdorff dimension for horseshoes’ (H. McCluskey and A. Manning, Ergod. Th. & Dynam. Sys. (1983) 3, 251–260), § 3 entitled ‘Continuity across a bifurcation’ should be deleted since the proof of theorem 3 there is wrong.The mistake is that does not in fact imply that δs → 1. This is because, for q = q0, the function is is only non-positive rather than negative and so is not strictly decreasing function of t.(Thus the pressure curve in figure 3 may, for q = q0, have become horizontal before t = l.) A similar mistake occurs in the second half of the same proof. Thus the claim of theorem 3 that the Hausdorff dimension of the basic set changes continuously in the bifurcation from Anosov to DA remains unproved. The rest of the paper is not affected.
Super persistent chaotic transients
Authors: Grebogi Celso , Ott Edward , Yorke James A. 
Published: September 2008

AbstractThe unstable-unstable pair bifurcation is a bifurcation in which two unstable fixed points or periodic orbits of the same period coalesce and disappear as a system paremeter is raised. For parameter values just above that at which unstable orbits are destroyed there can be chaotic transients. Then, as the bifurcation is approached from above, the average length of a chaotic transient diverges, and, below the bifurcation point, the chaotic transient may be regarded as having been converted into a chaotic attractor. It is argued that unstable-unstable pair bifurcations should be expected to occur commonly in dynamical systems. This bifurcation is an example of the crisis route to chaos. The most striking fact about unstable-unstable pair bifurcation crises is that long chaotic transients persist even for parameter values relatively far from the bifurcation point. These long-lived chaotic transients may prevent the time asymptotic state from being reached during experiments. An expression giving a lower bound for the average lifetime of a chaotic transient is derived and shown to agree well with numerical experiments. In particular, this bound on the average lifetime, (τ), satisfiesfor α near α*, where k1 and k2 are constants and α* is the value of the parameter a at which the crisis occurs. Thus, as a approaches α* from above, (τ) increases more rapidly than any power of (α − α*)−1. Finally, we discuss the effect of adding bounded noise (small random perturbations) on these phenomena and argue that the chaotic transients should be lengthened by noise.
Global shadowing of pseudo-Anosov homeomorphisms
Authors: Handel Michael 
Published: September 2008

AbstractWe prove that if f: M2→ M2 is pseudo-Anosov and if g ⋍ f then there is a closed subset X ⊂ M2 and a continuous surjection π: X→ M that is homotopic to inclusion such that f ° π = π ° g|X.
A counterexample to a positive entropy skew product generalization of the Pinsker conjecture
Authors: King Jonathan 
Published: September 2008

AbstractThe class of k-automorphisms is not contained in a certain class of skew products over a Bernoulli base. The non-identity fibre transformation in the skew is allowed to have positive or even infinite entropy. A difficulty presented by positive entropy is handled via an apparently new property of independent processes (lemma 7.24).
Relative equilibria of the four-body problem
Authors: Moeckel Richard 
Published: September 2008

AbstractBy employing a regularizing transformation, the problem of bifurcation of relative equilibria in the Newtonian 4-body problem is reduced to a study of an algebraic correspondence between real algebraic varieties. The finiteness theorems of algebraic geometry are used to find an upper bound for the number of affine equivalence classes of relative equilibria which holds for all masses in the complement of a proper, algebraic subset of the space of all masses.
Almost sure invariance principle for some maps of an interval
Authors: Ziemian Krystyna 
Published: September 2008

AbstractWe prove an almost sure invariance principle and a central limit theorem for the process , where f is a map of an interval with a non-positive Schwarzian derivative whose trajectories of critical points stay far from the critical points, and F is a measurable function with bounded p-variation (p ≥ 1).The almost sure invariance principle implies the Log-log laws, integral tests and a distributional type of invariance principle for the process .
On the Cr-closing lemma for flows on the torus T2
Authors: Gutierrez C. 
Published: September 2008

AbstractVector fields of , 1 ≤ r ≤ ∞, with non-trivial recurrent points are classified in two types, one of which we call the constant type inspired by the terminology of continued fractions. Let have finitely many singularities and p ∈ T2 be a non-wandering point of X. With the exception of the case when X is of constant type and, simultaneously, p is non-trivial recurrent, we prove that there exists arbitrarily close to X (in the Cr-topology) having a periodic trajectory through p.
Deciding eventual positivity of polynomials
Authors: Handelman David 
Published: September 2008

AbstractLet P and f be polynomials in several (real) variables, with P having no negative coefficients. We give necessary and sufficient conditions for there to exist a positive integer n with Pnf having no negative coefficients; roughly speaking, the conditions involve the behaviour of f as a function on the positive orthant, together with its behaviour on a boundary constructed from the supporting monomials of P. This completes a series of results due to Poincaré (1883), Meissner (1911), and Polyà (1927). The former discusses the one variable case, the latter two deal with the situation that the Newton polyhedra of both P and f be, respectively, standard hypercubes, standard simplices.
Rotation intervals for a class of maps of the real line into itself
Authors: Misiurewicz Michał 
Published: September 2008

AbstractWe study a class of maps of the real line into itself which are degree one liftings of maps of the circle and have discontinuities only of a special type. This class contains liftings of continuous degree one maps of the circle, lifting of increasing mod 1 maps and some maps arising from Newton's method of solving equations. We generalize some results known for the continuous case.
The Chebotarov theorem for Galois coverings of Axiom A flows
Authors: Parry William , Pollicott Mark 
Published: September 2008

AbstractWe consider G (Galois) coverings of Axiom A flows (restricted to basic sets) and prove an analogue of Chebotarev's theorem. The theorem provides an asymptotic formula for the number of closed orbits whose Frobenius class is a given conjugacy class in G. An application answers a question raised by J. Plante. The basic method is then extended to compact group extensions and applied to frame bundle flows defined on manifolds of variable negative curvature.
Fixed points of Lie group actions on surfaces
Authors: Plante J. F. 
Published: September 2008

AbstractLetGbe a connected finite-dimensional Lie group andMa compact surface. We investigate whether, for a givenGandM, every continuous action ofGonMmust have a fixed (stationary) point. It is shown that whenGis nilpotent andMhas non-zero Euler characteristic that every action ofGonMmust have a fixed point. On the other hand, it is shown that the non-abelian 2-dimensional Lie group (affine group of the line) acts without fixed points on every compact surface. These results make it possible to complete this investigation for Lie groups of dimension at most 3.
On orbits of unipotent flows on homogeneous spaces, II
Authors: Dani S. G. 
Published: September 2008

AbstractWe show that if (ut) is a one-parameter subgroup of SL (n, ℝ) consisting of unipotent matrices, then for any ε > 0 there exists a compact subset K of SL(n, ℝ)/SL(n, ℤ) such that the following holds: for any g ∈ SL(n, ℝ) either m({t ∈ [0, T] | utg SL (n, ℤ) ∈ K}) > (1 – ε)T for all large T (m being the Lebesgue measure) or there exists a non-trivial (g−1utg)-invariant subspace defined by rational equations.Similar results are deduced for orbits of unipotent flows on other homogeneous spaces. We also conclude that if G is a connected semisimple Lie group and Γ is a lattice in G then there exists a compact subset D of G such that for any closed connected unipotent subgroup U, which is not contained in any proper closed subgroup of G, we have G = DΓ U. The decomposition is applied to get results on Diophantine approximation.
A finiteness theorem for a dynamical class of entire functions
Authors: Goldberg Lisa R. , Keen Linda 
Published: September 2008

AbstractWe define a class Σ of entire functions whose covering properties are similar to those of rational maps. The set Σ is closed under composition of functions, and we show that when regarded as dynamical systems of the plane, the elements of Σ share many properties with rational maps. In particular, they have finite dimensional spaces of quasiconformal deformations, and they contain no wandering domains in their stable sets.
Vector fields with transverse foliations, II
Authors: Goodman Sue 
Published: September 2008

AbstractWhen does a non-singular flow on a 3-manifold have a 2-dimensional foliation everywhere transverse to it? A complete answer is given for a large class of flows, those with 1-dimensional hyperbolic chain recurrent set. We find a simple necessary and sufficient condition on the linking of periodic orbits of the flow.
Josephson's junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets
Authors: Hockett Kevin , Holmes Philip 
Published: September 2008

AbstractWe investigate the implications of transverse homoclinic orbits to fixed points in dissipative diffeomorphisms of the annulus. We first recover a result due to Aronsonet al.[3]: that certain such ‘rotary’ orbits imply the existence of an interval of rotation numbers in the rotation set of the diffeomorphism. Our proof differs from theirs in that we use embeddings of the Smale [61] horseshoe construction, rather than shadowing and pseudo orbits. The symbolic dynamics associated with the non-wandering Cantor set of the horseshoe is then used to prove the existence of uncountably many invariant Cantor sets (Cantori) of each irrational rotation number in the interval, some of which are shown to be ‘dissipative’ analogues of the order preserving Aubry-Mather Cantor sets found by variational methods in area preserving twist maps. We then apply our results to the Josephson junction equation, checking the necessary hypotheses via Melnikov's method, and give a partial characterization of the attracting set of the Poincaré map for this equation. This provides a concrete example of a ‘Birkhoff attractor’ [10].
On Hausdorff dimension of invariant sets for expanding maps of a circle
Authors: Urbański Mariusz 
Published: September 2008

AbstractGiven an orientation preserving C2 expanding mapping g: S1 → Sl of a circle we consider the family of closed invariant sets Kg(ε) defined as those points whose forward trajectory avoids the interval (0, ε). We prove that topological entropy of g|Kg(ε) is a Cantor function of ε. If we consider the map g(z) = zq then the Hausdorff dimension of the corresponding Cantor set around a parameter ε in the space of parameters is equal to the Hausdorff dimension of Kg(ε). In § 3 we establish some relationships between the mappings g|Kg(ε) and the theory of β-transformations, and in the last section we consider DE-bifurcations related to the sets Kg(ε).
Generating special Markov partitions for hyperbolic toral automorphisms using fractals
Authors: Bedford Tim 
Published: September 2008

AbstractWe show that given some natural conditions on a 3 × 3 hyperbolic matrix of integers A(det A = 1) there exists a Markov partition for the induced map A(x + ℤ3) = A(x)+ℤ3 on T3 whose transition matrix is (A−1)t. For expanding endomorphisms of T2 we construct a Markov partition so that there is a semiconjugacy from a full (one-sided) shift.
ω-limit sets for maps of the interval
Authors: Block Louis , Coven Ethan M. 
Published: September 2008

AbstractLet f denote a continuous map of a compact interval to itself, P(f) the set of periodic points of f and Λ(f) the set of ω-limit points of f. Sarkovskǐi has shown that Λ(f) is closed, and hence ⊆Λ(f), and Nitecki has shown that if f is piecewise monotone, then Λ(f)=. We prove that if x∈Λ(f)−, then the set of ω-limit points of x is an infinite minimal set. This result provides the inspiration for the construction of a map f for which Λ(f)≠.
From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems
Authors: Broer H. W. , Tangerman F. M. 
Published: September 2008

AbstractKupka-Smale like theorems are proven in the real analytic case, using existing perturbation schemes for the smooth case and the heat operator. As a consequence, a topological proof is obtained of Siegel's theorem on the generic divergence of normal form transformations.
Analytic models of pseudo-Anosov maps
Authors: Lewowicz Jorge , De Sá Eduardo Lima 
Published: September 2008

AbstractWe give a new proof of the existence of analytic models of pseudo-Anosov maps. The persistence properties of Thurston's maps ensure that any Co-perturbation of them presents all their dynamical features. Using Lyapunov functions of two variables we are able to choose certain analytic perturbations which do not add any new dynamical behaviour to the original pseudo-Anosov map.
Monotone twist mappings and the calculus of variations
Authors: Moser Jürgen 
Published: September 2008

AbstractIt is shown that a smooth area-preserving monotone twist mapping ϕ of an annulus A can be interpolated by a flow ϕt which is generated by a t-dependent Hamiltonian in ℝ × A having the period 1 in t and satisfying a Legendre condition. In other words, any such monotone twist mapping can be viewed as a section mapping for the extremals of variational problem on a torus:where F has period 1 in t and x and satisfies the Legendre condition Fẋẋ>0.
Perron units which are not Mahler measures
Authors: Boyd David W. 
Published: September 2008

AbstractThe Mahler measure M(α) of an algebraic integer α is the product of the absolute value of the conjugates of α which lie outside the unit circle. The quantity log M(α) occurs in ergodic theory as the entropy of an endomorphism of the torus. Adler and Marcus showed that if β = M(α) then β is a Perron number which is a unit if α is a unit. They asked whether the Perron number β whose minimal polynomial is tm −t −1 is the measure of any algebraic integer. We show here that the answer is negative for all m > 3.
Restricted orbit changes of ergodic ℤd-actions to achieve mixing and completely positive entropy
Authors: Fieldsteel Adam , Friedman N. A. 
Published: September 2008

AbstractWe show that for every ergodic ℤd-action T, there is a mixing ℤd-action S which is orbit equivalent to T via an orbit equivalence that is a weak a-equivalence for all a ≥ 1 and a strong b-equivalence for all b ∈ (0, 1). If T has positive entropy, then S can be taken to have completely positive entropy. If the dimension d is greater than one, the orbit equivalence may be taken to be bounded and a strong b-equivalence for all b > 0.
Multiple attractors in Newton's method
Authors: Hurley Mike 
Published: September 2008

AbstractFor eachd≥ 2 there exists a polynomialpwith real coefficients such that the associated Newton functionz–[p(z)/p′(z)] has 2d–2 distinct attracting periodic orbits in the complex plane. According to a theorem ofG. Julia, this is the maximal number of attracting orbits that any rational function of degreedcan possess.
Geometrical Markov coding of geodesics on surfaces of constant negative curvature
Authors: Series Caroline 
Published: September 2008

AbstractA natural geometrical representation of the geodesic flow on a surface M of constant negative curvature is given in which the base transformation is the shift on a (finite type) space of shortest words relative to a fixed generating set for π1(M) and the height function is the hyperbolic distance across a fundamental region for π1(M). This representation is obtained by comparing cutting sequences on M with generalised continued fraction expansions of endpoints on ℝ
On minimal self-joinings in topological dynamics
Authors: del Junco Andrés 
Published: September 2008

AbstractIf X is a compact metric space and T a homeomorphism of X we say (X, T) has almost minimal power joinings (AMPJ) if there is a dense GδX* in X such that for each finite set k, x∈(X*)k and l:k → ℤ−{0}, the orbit closure cl {} is a product of off-diagonals (POOD) on Xk. By an offdiagonal on Xk′, k′k we mean a set of the form (⊗,j∈k′Tm(j))Δ, Δ the diagonal in Xk′, m:k′→ℤ any function, and by a POOD on Xk we mean that k is split into subsets k′, on each Xk′ we put an off-diagonal and then we take the product of these.We show that examples of AMPJ exist and that this definition leads to a theory completely analogous to Rudolph's theory of minimal self-joinings in ergodic theory. In particular if (X, T) has AMPJ the automorphism group of T is {Tn}, T has only almost 1-1 factors (other than the trivial one) and the automorphism group and factors of ⊕i ∊ kT, k finite or countably infinite, can be very explicitly described. We also discuss ℝ-actions.
Expansive dynamics on zero-dimensional groups
Authors: Kitchens Bruce P. 
Published: September 2008

AbstractIf X is a compact, zero-dimensional group and T is an expansive, transitive automorphism then (X, T) is shown to be topologically conjugate to a full shift on finitely many symbols.The problem of classifying such automorphisms up to simultaneous algebraic isomorphism and topological conjugacy is discussed but not solved. It is proved that for any entropy there are only finitely many such equivalence classes. When the entropy is log p for a prime p, there is only one equivalence class. All are then equivalent to
The rate of mixing for geodesic and horocycle flows
Authors: Ratner Marina 
Published: September 2008

AbstractUsing elementary methods we show that for every unitary representation π7 of G = SL(2, ℝ) with no non-zero invariant vectors the matrix coefficients 〈 π(a(t))v, w 〉 ofdecay exponentially fast for any vectors v, w Holder continuous in the direction of the rotation subgroup of G.
A modulus of 3-dimensional vector fields
Authors: Togawa Y. 
Published: September 2008

AbstractIn this paper, we prove that μ/λ is a modulus for a Šilnikov system with eigenvalues λ and −μ ± iω. To prove this we define a number using knot and link invariants of periodic orbits, which is related to the ratio of eigenvalues μ/λ.
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
Authors: Dumortier F. , Roussarie R. , Sotomayor J. 
Published: September 2008

AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to
Diffeomorphisms on surfaces with a finite number of moduli
Authors: de Melo W. , van Strien S.J. 
Published: September 2008

AbstractThis paper generalises the well known structural stability theorem which says that a diffeomorphism is structurally stable if it is Axiom A and if all invariant manifolds are transversal to each other.If these transversality conditions are not satisfied then the diffeomorphism not only fails to be stable, but also this gives rise to the appearance of moduli. That is, one needs several real parameters to parameterise all conjugacy classes of nearby diffeomorphisms. (The minimum number of parameters needed is called the number of moduli).Here we deal with diffeomorphisms on two dimensional manifolds, whose asymptotic dynamics are well understood (the class of Axiom A diffeomorphisms). The main result characterises those Axiom A diffeomorphisms which have a finite number of moduli. This result can be regarded as a generalisation of the structural stability theorem. From the proofs it follows that the dynamics of these diffeomorphisms can also be well understood.In the proof of our main theorem we need certain invariant foliations to be quite smooth. In an appendix we prove a differentiable version of the Lambda Lemma.
A bound for the fixed point index of area-preserving homeomorphisms of two-manifolds
Authors: Pelikan Stephan , Slaminka Edward E. 
Published: September 2008

AbstractThe study of area preserving maps of manifolds has an extensive history in the theory of dynamical systems. One interest has been in the behaviour of such maps near an isolated fixed point. In 1974 Carl Simon proved the existence of an upper bound for the index of an isolated fixed point for Ck area preserving diffeomorphisms of a surface. We extend his result to homeomorphisms of an orientable two manifold. The proof utilizes the notion of free modification, developed by Morton Brown, and enlarges the scope of the problem to the consideration of ‘nice’ measures, i.e. uniformly equivalent to Lebesgue measure on compact sets. By suitably modifying the homeomorphism and the measure, we obtain the following theorem.
Finitely presented dynamical systems
Authors: Fried David 
Published: September 2008

AbstractWe extend results of Bowen and Manning on systems with good symbolic dynamics. In particular we identify the class of dynamical systems that admit Markov partitions. For these systems the Manning-Bowen method of counting periodic points is explained in terms of topological coincidence numbers. We show, in particular, that an expansive system with a finite cover by rectangles has a rational zeta function.
On the generic existence of homoclinic points
Authors: Oliveira Fernando 
Published: September 2008

AbstractThis work is concerned with the generic existence of homoclinic points for area preserving diffeomorphisms of compact orientable surfaces. We give a shorter proof of Pixton's theorem that shows that, Cr-generically, an area preserving diffeomorphism of the two sphere has the property that every hyperbolic periodic point has transverse homoclinic points. Then, we extend Pixton's result to the torus and investigate certain generic aspects of the accumulation of the invariant manifolds all over themselves in the case of symplectic diffeomorphisms of compact manifolds.