bluuebunny/crossref_metadata_2025_split huggingface dataset:
The bifurcation of homoclinic orbits of maps of the interval
Authors: Block Louis , Hart David 
Published: September 2008

AbstractRelationships involving homoclinic orbits of various periods and the Sarkovskii stratification are given and corresponding bifurcation properties are derived. It is shown that if a continuous map has one homoclinic periodic orbit, it has infinitely many. In any family of C1 maps going from zero to positive entropy, infinitely many homoclinic bifurcations occur, involving periods which are successively smaller powers of two.
On uniformly distributed orbits of certain horocycle flows
Authors: Dani S. G. 
Published: September 2008

AbstractLet(where t ε ℝ) and let μ be the G-invariant probability measure on G/Γ. We show that if x is a non-periodic point of the flow given by the (ut)-action on G/Γ then the (ut)-orbit of x is uniformly distributed with respect to μ; that is, if Ω is an open subset whose boundary has zero measure, and l is the Lebesque measure on ℝ then, as T→∞, converges to μ(Ω).
Isentropic fitting of Anosov automorphisms
Authors: Fried David 
Published: September 2008

AbstractIn response to a question of Newhouse, we show that in many cases an Anosov automorphism can be uniformly approximated by a Smale diffeomorphism of the same topological entropy. We conjecture this can be done whenever the automorphism is sufficiently hyperbolic.A three-dimensional example is given that suggests this approximation is not always possible.
Some remarks on Birkhoff and Mather twist map theorems
Authors: Katok A. 
Published: September 2008

AbstractA recent result of J. Mather [1] about the existence of quasi-periodic orbits for twist maps is derived from an appropriately modified version of G. D. Birkhoff's classical theorem concerning periodic orbits. A proof of Birkhoff's theorem is given using a simplified geometric version of Mather's arguments. Additional properties of Mather's invariant sets are discussed.
On the subsystems of topological Markov chains
Authors: Krieger Wolfgang 
Published: September 2008

AbstractLet SA be an irreducible and aperiodic topological Markov chain. If SĀ is an irreducible and aperiodic topological Markov chain, whose topological entropy is less than that of SA, then there exists an irreducible and aperiodic topological Markov chain, whose topological entropy equals the topological entropy at SĀ, and that is a subsystem of SA. If S is an expansive homeomorphism of the Cantor discontinuum, whose topological entropy is less than that of SA, and such that for every j∈ℕ the number of periodic points of least period j of S is less than or equal to the number of periodic points of least period j of SA, then S is topological conjugate to a subsystem of SA.
Entropy and closed geodesies
Authors: Katok A. 
Published: September 2008

AbstractWe study asymptotic growth of closed geodesies for various Riemannian metrics on a compact manifold which carries a metric of negative sectional curvature. Our approach makes use of both variational and dynamical description of geodesies and can be described as an asymptotic version of length-area method. We also obtain various inequalities between topological and measure-theoretic entropies of the geodesic flows for different metrics on the same manifold. Our method works especially well for any metric conformally equivalent to a metric of constant negative curvature. For a surface with negative Euler characteristics every Riemannian metric has this property due to a classical regularization theorem. This allows us to prove that every metric of non-constant curvature has strictly more close geodesies of length at most T for sufficiently large T then any metric of constant curvature of the same total area. In addition the common value of topological and measure-theoretic entropies for metrics of constant negative curvature with the fixed area separates the values of two entropies for other metrics with the same area.
Examples of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behaviour
Authors: Przytycki Feliks 
Published: September 2008

AbstractWe find very simple examples of C∞-arcs of diffeomorphisms of the two-dimensional torus, preserving the Lebesgue measure and having the following properties: (1) the beginning of an arc is inside the set of Anosov diffeomorphisms; (2) after the bifurcation parameter every diffeomorphism has an elliptic fixed point with the first Birkhoff invariant non-zero (the KAM situation) and an invariant open area with almost everywhere non-zero Lyapunov characteristic exponents, moreover where the diffeomorphism has Bernoulli property; (3) the arc is real-analytic except on two circles (for each value of parameter) which are inside the Bernoulli property area.
Bifurcation of an attracting invariant circle: a Denjoy attractor
Authors: Hall Glen R. 
Published: September 2008

AbstractWe construct an example of a C∞ diffeomorphism of an annulus into itself which has an attracting invariant circle such that the map restricted to this circle has no periodic points and no dense orbits. By studying two parameter families of maps of the plane which undergo Hopf bifurcation, particularly the set of parameter values for which the rotation number is irrational, we see that the above example can be considered as a ‘worst case’ of the loss of smoothness of an attracting invariant circle without periodic orbits.
On a construction of unitary cocycles and the representation theory of amenable groups
Authors: Sutherland Colin E. 
Published: September 2008

AbstractIf K is a countable amenable group acting freely and ergodically on a probability space (Γ, μ), and G is an arbitrary countable amenable group, we construct an injection of the space of unitary representations of G into the space of unitary 1-cocyles for K on (Γ, μ); this injection preserves intertwining operators. We apply this to show that for many of the standard non-type-I amenable groups H, the representation theory of H contains that of every countable amenable group.
Errata to ‘A proof of Pesin's formula’
Authors: Mañé R. 
Published: September 2008

In the paper ‘A proof of Pesin's formula’ (R. Mañé, Ergod. Th. & Dynam. Sys. (1981), 1, 95–102) there are some minor but misleading mistakes. The following corrections are necessary:(1) On page 99, inequality (11) states:It should read:The first inequality is obviously false in general. The second one is an immediate corollary of Oseledec's theorem. This misprint is of no consequence because in the rest of the paper we always used the correct inequality.
Bifurcation and chain recurrence
Authors: Hurley M. 
Published: September 2008

AbstractWe show that there is a residual subset of the set of C1 diffeomorphisms on any compact manifold at which the mapis continuous. As this number is apt to be infinite, we prove a localized version, which allows one to conclude that if f is in this residual set and X is an isolated chain component for f, then(i) there is a neighbourhood U of X which isolates it from the rest of the chain recurrent set of f, and(ii) all g sufficiently C1 close to f have precisely one chain component in U, and these chain components approach X as g approaches f.(ii) is interpreted as a generic non-bifurcation result for this type of invariant set.
Hausdorff dimension for horseshoes
Authors: McCluskey Heather , Manning Anthony 
Published: September 2008

AbstractWe shall measure how thick a basic set of a C1 axiom A diffeomorphism of a surface is by the Hausdorff dimension of its intersection with an unstable manifold. This depends continuously on the diffeomorphism. Generically a C2 diffeomorphism has attractors whose Hausdorff dimension is not approximated by the dimension of its ergodic measures.
The C1 Closing Lemma, including Hamiltonians
Authors: Pugh Charles C. , Robinson Clark 
Published: September 2008

AbstractAn Axiom of Lift for classes of dynamical systems is formulated. It is shown to imply the Closing Lemma. The Lift Axiom is then verified for dynamical systems ranging from C1 diffeomorphisms to C1 Hamiltonian vector fields.
The orbit of a Hölder continuous path under a hyperbolic toral automorphism
Authors: Irwin M. C. 
Published: September 2008

AbstractLet f:T3→T3 be a hyperbolic toral automorphism lifting to a linear automorphism with real eigenvalues. We prove that there is a Hölder continuous path in T3 whose orbit-closure is 1-dimensional. This strengthens results of Hancock and Przytycki concerning continuous paths, and contrasts with results of Franks and Mañé concerning rectifiable paths.
Constant-to-one and onto global maps of homomorphisms between strongly connected graphs
Authors: Nasu Masakazu 
Published: September 2008

AbstractThe global maps of homomorphisms of directed graphs are very closely related to homomorphisms of a class of symbolic dynamical systems called subshifts of finite type. In this paper, we introduce the concepts of ‘induced regular homomorphism’ and ‘induced backward regular homomorphism’ which are associated with every homomorphism between strongly connected graphs whose global map is finite-to-one and onto, and using them we study the structure of constant-to-one and onto global maps of homorphisms between strongly connected graphs and that of constant-to-one and onto homomorphisms of irreducible subshifts of finite type. We determine constructively, up to topological conjugacy, the subshifts of finite type which are constant-to-one extensions of a given irreducible subshift of finite type. We give an invariant for constant-to-one and onto homomorphisms of irreducible subshifts of finite type.
Croissance des boules et des géodésiques fermées dans les nilvariétés
Authors: Pansu Pierre 
Published: September 2008

AbstractIf (M, g) is a riemannian nilmanifold, the homothetic metrics εg˜ on the universal cover M converge in the sense of Gromov for small ε. In this convergence the volume of balls and the number of closed geodesies go to a limit, and precise asymptotic estimates are given for these numbers.
Strong shift equivalence of 2 × 2 matrices of non-negative integers
Authors: Baker Kirby A. 
Published: September 2008

AbstractThe concept of strong shift equivalence of square non-negative integral matrices has been used by R. F. Williams to characterize topological isomorphism of the associated topological Markov chains. However, not much has been known about sufficient conditions for strong shift equivalence even for 2×2 matrices (other than those of unit determinant). The main theorem of this paper is: If A and B are positive 2×2 integral matrices of non-negative determinant and are similar over the integers, then A and B are strongly shift equivalent.
Topological minimal self-joinings
Authors: Markley Nelson G. 
Published: September 2008

AbstractThere is an interesting duality between some of the concepts of ergodic theory and those of topological dynamics. This paper is a first attempt at developing a topological analogue to the measure-theoretic notion of a transformation having minimal self-joinings. The main problem is to understand the dynamics of the composition of a cartesian product of powers of a transformation having topological minimal self-joinings with a compact permutation of the coordinates. Most of the results are about the minimal subsets of such a composition.
Immediate conditional hyperbolicity in dynamical systems
Authors: Rosenblatt Joseph , Swanson Richard 
Published: September 2008

AbstractFor many diffeomorphisms of a compact manifold X, eventual conditional hyperbolicity implies immediate conditional hyperbolicity in some (possibly new) Finsler structures. That is, if A and B are vector bundle isomorphisms over the mapping ƒ of the base X, such that uniformly on X, then there exist new norms for A and B such that uniformly on X, whenever the mapping ƒ satisfies the condition that there exist infinitely many N ≥ 1 such that any ƒ-invariant. For example, this condition on ƒ holds if any one of the following conditions holds: (1) ƒ is periodic; (2) ƒ is periodic on its non-wandering set; (3) ƒ has a finite non-wandering set (for example, ƒ is a Morse-Smale diffeomorphism); (4) ƒ is an almost periodic mapping of a connected base X; (5) ƒ is a mapping of the circle with no periodic points; or (6) ƒ and all its powers are uniquely ergodic. We consider various types of eventually conditionally hyperbolic systems and describe sufficient conditions on ƒ to have immediate conditional hyperbolicity of these systems in some new Finsler structures. Thus, for a sizable class of dynamical systems, we settle, in the affirmative, a question raised by Hirsch, Pugh, and Shub.
On orbits of unipotent flows on homogeneous spaces
Authors: Dani S. G. 
Published: September 2008

AbstractLet G be a connected Lie group and let Γ be a lattice in G (not necessarily co-compact). We show that if (ut) is a unipotent one-parameter subgroup of G then every ergodic invariant (locally finite) measure of the action of (ut) on G/Γ is finite. For ‘arithmetic lattices’ this was proved in [2]. The present generalization is obtained by studying the ‘frequency of visiting compact subsets’ for unbounded orbits of such flows in the special case where G is a connected semi-simple Lie group of ℝ-rank 1 and Γ is any (not necessarily arithmetic) lattice in G.
Combined structural and topological stability are equivalent to Axiom A and the strong transversality condition
Authors: Hurley Mike 
Published: September 2008

AbstractThe purpose of this paper is to develop necessary conditions for a diffeomorphism to be topologically stable (lower semistable). Our results combine with a recent theorem of R. Mañé and with earlier results of J. Robbin, C. Robinson, and Z. Nitecki to give a complete characterization of diffeomorphisms of compact manifolds that are both topologically and structurally stable: they are precisely the Axiom A diffeomorphisms that satisfy the strong transversality condition.
Lorenz knots are prime
Authors: Williams R. F. 
Published: September 2008

AbstractLorenz knots are the periodic orbits of a certain geometrically defined differential equation in ℝ3. This is called the ‘geometric Lorenz attractor’ as it is only conjecturally the real Lorenz attractor. These knots have been studied by the author and Joan Birman via a ‘knot-holder’, i.e. a certain branched two-manifold H. To show such knots are prime we suppose the contrary which implies the existence of a splitting sphere, S2. The technique of the proof is to study the intersection S2∩H. A novelty here is that S2∩H is likewise branched.
One-parameter automorphism groups of operator algebras allowing spectral projections
Authors: Elliott George A. , Zsidó László 
Published: September 2008

AbstractThe property of a one-parameter C*- (or W*-) dynamical system that the spectral subspaces corresponding to the three subsets (−∞, 0), {0}, and (0, +∞) add up to the whole algebra is reformulated. If the C*-algebra is prime (or the W*-algebra is a factor), an equivalent property is that the spectrum is finite.
Uncountably many topological models for ergodic transformations
Authors: Glasner S. , Rudolph D. 
Published: September 2008

AbstractGiven a topological process (X, µ, T) where T is a homeomorphism of the compact metric space X which preserves the probability measure µ and is ergodic, we show that there exists an uncountable family {(Xi, µi, Ti)}i∈I of topological processes such that for every i, (Xi, µi, Ti) is measure-theoretically isomorphic to (X, µ, T) but for every i ≠ j, (Xi, µi, Ti) and (Xj, µj, Tj) are not almost topologically conjugate.
The Lyapunov dimension of a nowhere differentiable attracting torus
Authors: Kaplan James L. , Mallet-Paret John , Yorke James A. 
Published: September 2008

AbstractThe fractal dimension of an attracting torusTkin×Tkis shown to be almost always equal to the Lyapunov dimension as predicted by a previous conjecture. The cases studied here can have several Lyapunov numbers greater than 1 and several less than 1
The entropies of topological Markov shifts and a related class of algebraic integers
Authors: Lind D. A. 
Published: September 2008

AbstractWe give an algebraic characterization of the class of spectral radii of aperiodic non-negative integral matrices, and describe a method of constructing all such matrices with given spectral radius. The logarithms of the numbers in are the entropies of mixing topological Markov shifts. There is an arithmetic structure to , including factorization into irreducibles in only finitely many ways. This arithmetic structure has dynamical consequences, such as the impossibility of factoring the p-shift into a direct product of nontrivial homeomorphisms for prime p.
Twist sets for maps of the circle
Authors: Misiurewicz Michał 
Published: September 2008

AbstractLet f be a continuous map of degree one of the circle onto itself. We prove that for every number a from the rotation interval of f there exists an invariant closed set A consisting of points with rotation number a and such that f restricted to A preserves the order. This result is analogous to the one in the case of a twist map of an annulus.
The backward continued fraction map and geodesic flow
Authors: Adler Roy L. , Flatto Leopold 
Published: September 2008

AbstractThe ‘backward continued fraction’ map studied by A. Reyni is defined by y = g(x) where g(x) equals the fractional part of 1/(1−x) for 0 < x < 1. We show that it is a factor map of a special cross-section map for the geodesic flow on the unit tangent bundle of the modular surface. This gives an alternative derivation of the fact that this map preserves the infinite measure dx/x on the unit interval.
Minimal sets on tori
Authors: Berend Daniel 
Published: September 2008

AbstractLet Σ be a commutative semigroup of continuous endomorphisms of the r-dimensional torus. Generalizing a result of Furstenberg dealing with the circle group, necessary and sufficient conditions are given here for Σ to possess the following property: Any Σ-minimal set consists of torsion elements. Semigroups not having this property are shown to admit minimal sets of positive Hausdorff dimension.
Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension
Authors: Broer H. W. , Vegter G. 
Published: September 2008

AbstractA specific singularity of a vector field on is considered, of codimension 2 in the dissipative case and of codimension 1 in the conservative case. In both contexts in generic unfoldings the existence is proved of subordinate Šil'nikov bifurcations, which have codimension 1. Special attention is paid to the C∞-flatness of this subordinate phenomenon.
A criterion for the positivity of the Liapunov characteristic exponent
Authors: Cornelis Eric , Wojtkowski Maciej 
Published: September 2008

AbstractWe formulate sufficient conditions under which, for a finite subset of SL (2, ℝ), the maximal Liapunov exponent is positive. These conditions are based on the notion of compatible hyperbolicity. We then give an analytical formulation of such a condition and we apply this criterion to prove mixing properties of a particular transformation of the two-dimensional torus.
Transitivity and invariant measures for the geometric model of the Lorenz equations
Authors: Robinson Clark 
Published: September 2008

AbstractThis paper concerns perturbations of the geometric model of the Lorenz equations and their associated one-dimensional Poincaré maps. R. Williams has shown that if a map of the interval of the type arising from the Lorenz equations satisfies f′(x) > 2½ everywhere except at the discontinuity then f is locally eventually onto (l.e.o.) and so topologically transitive [14]. We show roughly that if are the end points of the interval, and their iterates stay on the same side of the point of discontinuity for 0 ≤ j ≤ k, and f′(x) > 21/(k+1) everywhere, then f is l.e.o. Secondly, we show that the one-dimensional Poincaré map of any Cr perturbation of the geometric model (for large enough r) has an ergodic measure which is equivalent to Lebesgue measure. This result follows by showing it is C1+α and satisfies a theorem of Keller, Wong, Lasota, Li & Yorke.
The Perron-Frobenius operator in spaces of smooth functions on an interval
Authors: Szewc B. 
Published: September 2008

AbstractThe densities of invariant measures for Misiurewicz maps and Lasota-Yorke maps of class Cr are of class Cr-1 on certain intervals (forming the partition of an interval in case of Misiurewicz maps). For these maps the Perron-Frobenius operator has an unambiguous decomposition into the sum of projections onto eigenspaces (multiplied by the eigenvalues) and a remainder operator. The remainder operator has spectral radius less than one in certain spaces of smooth functions.
On the Bernoulli property for rational maps
Authors: Mañé Ricardo 
Published: September 2008

AbstractEvery rational function ƒ with degree has a unique invariant probability ƒƒ that maximizes entropy. It has been conjectured that the system (ƒ, μƒ) is equivalent to the one sided Bernoulli shift . In this paper we prove that there exists m >0 such that (ƒm, ƒƒ) is equivalent to .
Characterization of MorseSmale isotopy classes on surfaces
Authors: Fernando Luiz , Da Rocha C. 
Published: September 2008

AbstractIn this paper we use Thurston's work on the dynamics of diffeomorphisms on surfaces to show that a diffeomorphism ƒ on a surface is isotopic to a Morse- Smale one if and only if the growth rate of the length of the words representing elements of the fundamental group under iteration by ƒ is one. Morse-Smale isotopy classes are also shown to be the same as Nielsen's algebraically finite type.
A Morse equation in Conley's index theory for semiflows on metric spaces
Authors: Rybakowski Krzysztof P. , Zehnder Eduard 
Published: September 2008

AbstractGiven a compact (two-sided) flow, an isolated invariant set S and a Morse-decomposition (M1, …, Mn) of S, there is a generalized Morse equation, proved by Conley and Zehnder, which relates the Alexander-Spanier cohomology groups of the Conley indices of the sets Mi and S with each other. Recently, Rybakowski developed the technique of isolating blocks and extended Conley's index theory to a class of one-sided semiflows on non-necessarily compact spaces, including e.g. semiflows generated by parabolic equations. Using these results, we discuss in this paper Morse decompositions and prove the above-mentioned Morse equation not only for arbitrary homology and cohomology groups, but also in this more general semiflow setting.
Invariant families of cones and Lyapunov exponents
Authors: Wojtkowski Maciej 
Published: September 2008

AbstractWe show that in several cases preservation of cones leads to non-vanishing of (some) Lyapunov exponents. It gives simple and effective criteria for nonvanishing of the exponents, which is demonstrated on the example of the billiards studied by Bunimovich. It is also shown that geodesic flows on manifolds of non-positive sectional curvature can be treated from this point of view.
Some entire functions with multiply-connected wandering domains
Authors: Baker I. N. 
Published: September 2008

AbstractA component U of the complement of the Julia set of an entire function ƒ is a wandering domain if the sets ƒn(U) are mutually disjoint, where n ∈ℕ and ƒn is the n-th iterate of ƒ. Examples are given of entire ƒ of order , which have multiply-connected wandering domains. An example is given where the connectivity is infinite.
The characterization of differential operators by locality: abstract derivations
Authors: Batty C. J. K. , Robinson D. W. 
Published: September 2008

AbstractLet δ be a closed *-derivation on a commutative C*-algebra , suppose that is dense in for some n = 1, 2, …, ∞, and let be a linear operator satisfying the locality conditionIt is shown that , for some finite integer p≤n and functions lm on X. Estimates on the coefficients lm are obtained and applied to flows and local flows.