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1.
The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weak mixing suspension flows over substitution automorphisms, which yield information about the “fractal” structure of these measures. The main results are, first, a Hölder estimate for the spectral measure of almost all suspension flows with a piecewise constant roof function; second, a log-Hölder estimate for self-similar suspension flows; and, third, a Hölder asymptotic expansion of the spectral measure at zero for such flows. Our second result implies log-Hölder estimates for the spectral measures of translation flows along stable foliations of pseudo-Anosov automorphisms. A key technical tool in the proof of the second result is an “arithmetic-Diophantine” proposition, which has other applications. In Appendix A this proposition is used to derive new decay estimates for the Fourier transforms of Bernoulli convolutions. 相似文献
2.
In dynamical systems theory, a standard method for passing from discrete time to continuous time is to construct the suspension
flow under a roof function. In this paper, we give conditions under which statistical laws, such as the central limit theorem
and almost sure invariance principle, for the underlying discrete time system are inherited by the suspension flow. As a consequence,
we give a simpler proof of the results of Ratner (1973) and recover the results of Denker and Philipp (1984) for Axiom A flows.
Morcover, we obtain several new results for nonuniformly and partially hyperbolic flows, including frame flows on negatively
curved manifolds satisfying a pinching condition. 相似文献
3.
4.
K. M. Madden 《Israel Journal of Mathematics》1998,103(1):67-92
Cocycles ofZ
m actions on compact metric spaces provide a means for constructingR
m actions or flows, called suspension flows. It is known that allR
m flows with a free dense orbit have an almost one-to-one extension which is a suspension flow. Whenm=1, examples of cocycles are easy to construct; there is a one-to-one correspondence between cocycles and real valued continuous
functions. However, whenm>1 the construction of examples of cocycles becomes more problematic. The only existing class of examples, the close to linear
cocycles, have strong linearity properties and are well understood. In fact, when theZ
m action is uniquely ergodic, all cocycles are close to linear. We will show that in general this need not be the case. We
present a method, suggested to us by Hillel Furstenberg, for constructing examples of cocycles whenm>1 and use this method to construct a non close to linear cocycle on a minimalZ
2 action. 相似文献
5.
Entropy of flows, revisited 总被引:2,自引:0,他引:2
We introduce a concept of measure-theoretic entropy for flows and study its invariance under measure-theoretic equivalences. Invariance properties of the corresponding topological entropy is studied too. We also answer a question posed by Bowen-Walters in [3] concerning the equality between the topological entropy of the time-one map of an expansive flow and the time-one map of its symbolic suspension.Partially supported by FAPESP-Brasil, Grant #96/11671-6.Partially supported by CNPq-Brasil, Grant #300557/89-2. 相似文献
6.
Masayuki Asaoka 《Inventiones Mathematicae》2008,174(2):435-462
We show that any topologically transitive codimension-one Anosov flow on a closed manifold is topologically equivalent to
a smooth Anosov flow that preserves a smooth volume. By a classical theorem due to Verjovsky, any higher-dimensional codimension-one
Anosov flow is topologically transitive. Recently, Simić showed that any higher-dimensional codimension-one Anosov flow that
preserves a smooth volume is topologically equivalent to the suspension of an Anosov diffeomorphism. Therefore, our result
gives a complete classification of codimension-one Anosov flows up to topological equivalence in higher dimensions. 相似文献
7.
Kenneth R. Driessel 《Linear algebra and its applications》2007,421(1):69-84
Driessel [K.R. Driessel, Computing canonical forms using flows, Linear Algebra Appl 379 (2004) 353-379] introduced the notion of quasi-projection onto the range of a linear transformation from one inner product space into another inner product space. Here we introduce the notion of quasi-projection onto the intersection of the ranges of two linear transformations from two inner product spaces into a third inner product space. As an application, we design a new family of iso-spectral flows on the space of symmetric matrices that preserves zero patterns. We discuss the equilibrium points of these flows. We conjecture that these flows generically converge to diagonal matrices. We perform some numerical experiments with these flows which support this conjecture. We also compare our zero-preserving flows with the Toda flow. 相似文献
8.
S. R. Fenley 《Commentarii Mathematici Helvetici》1998,73(2):259-297
In this article we study the topology of Anosov flows in 3-manifolds. Specifically we consider the lifts to the universal
cover of the stable and unstable foliations and analyze the leaf spaces of these foliations. We completely determine the structure
of the non Hausdorff points in these leaf spaces. There are many consequences: (1) when the leaf spaces are non Hausdorff,
there are closed orbits in the manifold which are freely homotopic, (2) suspension Anosov flows are, up to topological conjugacy,
the only Anosov flows without free homotopies between closed orbits, (3) when there are infinitely many stable leaves (in
the universal cover) which are non separated from each other, then we produce a torus in the manifold which is transverse
to the Anosov flow and therefore is incompressible, (4) we produce non Hausdorff examples in hyperbolic manifolds and derive
important properties of the limit sets of the stable/unstable leaves in the universal cover.
Received: March 13, 1997 相似文献
9.
David Fried 《Commentarii Mathematici Helvetici》1982,57(1):237-259
We analyze the dynamics of diffeomorphisms in terms of their suspension flows. For many Axion A diffeomorphisms we find simplest
representatives in their flow equivalence class and so reduce flow equivalence to conjugacy. The zeta functions of maps in
a flow equivalence class are correlated with a zeta function ζ
H
for their suspended flow. This zeta function is defined for any flow with only finitely many closed orbits in each homology
class, and is proven rational for Axiom A flows. The flow equivalence of Anosov diffeomorphisms is used to relate the spectrum
of the induced map on first homology to the existence of fixed points. For Morse-Smale maps, we extend a result of Asimov
on the geometric index.
Partially supported by MCS 76-08795. 相似文献
10.
M. A. Brutyan P. L. Krapivsky 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1992,43(4):715-725
We have shown that unidirectional flows of viscoelastic fluids are mathematically equivalent to plane potential flows of a fictitious gas. The classification of type and some exact solutions of the equations describing fictitious gas flows are presented. The Prandtl-Mayer flow and its viscoelastic counterpart is discussed in more details in connection with the Sternberg-Koiter paradox. 相似文献
11.
Bonatti and Langevin constructed an Anosov flow on a closed 3-manifold with a transverse torus intersecting all orbits except one [C. Bonatti, R. Langevin, Un exemple de flot d'Anosov transitif transverse à un tore et non conjugué à une suspension, Ergodic Theory Dynam. Systems 14 (4) (1994), 633-643]. We shall prove that these flows cannot be constructed on closed 4-manifolds. More precisely, there are no Anosov flows on closed 4-manifolds with a closed, incompressible, transverse submanifold intersecting all orbits except finitely many closed ones. The proof relies on the analysis of the trace of the weak invariant foliations of the flow on the transverse submanifold. 相似文献
12.
We study minimal flows by studying a universal minimal flow, invariant closed equivalence relations (icers) on it, subgroups
of its group of automorphisms, and the interplay among these objects. As examples of this approach we discuss and give short
proofs of some standard results on distal flows. We end with a statement of the Furstenberg structure theorem from this point
of view. 相似文献
13.
We consider two incompressible viscous fluid flows interacting through thin non-Newtonian boundary layers of higher Reynolds? number. We study the asymptotic behaviour of the problem, with respect to the vanishing thickness of the layers, using Γ-convergence methods. We derive general interfacial boundary conditions between the two fluid flows. These boundary conditions are specified for some particular cases including periodic or fractal structures of layers. 相似文献
14.
We look at the problem of optimizing complex operations with incomplete information where the missing information is revealed indirectly and imperfectly through historical decisions. Incomplete information is characterized by missing data elements governing operational behavior and unknown cost parameters. We assume some of this information may be indirectly captured in historical databases through flows characterizing resource movements. We can use these flows or other quantities derived from these flows as “numerical patterns” in our optimization model to reflect some of the incomplete information. We develop our methodology for representing information in resource allocation models using the concept of pattern regression. We use a popular goodness-of-fit measure known as the Cramer–Von Mises metric as the foundation of our approach. We then use a hybrid approach of solving a cost model with a term known as the “pattern metric” that minimizes the deviations of model decisions from observed quantities in a historical database. We present a novel iterative method to solve this problem. Results with real-world data from a large freight railroad are presented. 相似文献
15.
We construct the canonical solitons, in terms of Cabezas-Rivas and Topping, associated with some generalized Ricci flows. 相似文献
16.
We consider interval exchange transformations of periodic type and construct different classes of ergodic cocycles of dimension?1 over this special class of IETs. Then using Poincaré sections we apply this construction to obtain the recurrence and ergodicity for some smooth flows on non-compact manifolds which are extensions of multivalued Hamiltonian flows on compact surfaces. 相似文献
17.
18.
Fernando Muro 《Transactions of the American Mathematical Society》2005,357(9):3623-3653
Crossed and quadratic modules are algebraic models of the 2-type and the 3-type of a space, respectively. In this paper we compute a purely algebraic suspension functor from crossed to quadratic modules which sends a 2-type to the 3-type of its suspension. We also give some applications in homotopy theory and group theory.
19.
We define a class of geometric flows on a complete Khler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equations, derivative nonlinear Schrdinger equations etc. Furthermore, we consider the existence for these flows from S~1into a complete Khler manifold and prove some local and global existence results. 相似文献
20.
We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies. 相似文献