共查询到20条相似文献,搜索用时 31 毫秒
1.
Konstantin Medynets 《Comptes Rendus Mathematique》2006,342(1):43-46
We prove that every Cantor aperiodic system is homeomorphic to the Vershik map acting on the space of infinite paths of an ordered Bratteli diagram and give several corollaries of this result. To cite this article: K. Medynets, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
2.
We prove an index theorem for foliated manifolds. We do so by constructing a push forward map in cohomology for a k-oriented map from an arbitrary manifold to the space of leaves of an oriented foliation, and by constructing a Chern–Connes character from the k-theory of the compactly supported smooth functions on the holonomy groupoid of the foliation to the Haefliger cohomology of the foliation. Combining these with the Connes–Skandalis topological index map and the classical Chern character gives a commutative diagram from which the index theorem follows immediately. 相似文献
3.
Eduard Looijenga 《Inventiones Mathematicae》2009,177(1):213-233
The period map for cubic fourfolds takes values in a locally symmetric variety of orthogonal type of dimension 20. We determine
the image of this period map (thus confirming a conjecture of Hassett) and give at the same time a new proof of the theorem
of Voisin that asserts that this period map is an open embedding. An algebraic version of our main result is an identification
of the algebra of SL (6,ℂ)-invariant polynomials on the representation space Sym 3(ℂ6)* with a certain algebra of meromorphic automorphic forms on a symmetric domain of orthogonal type of dimension 20. We also
describe the stratification of the moduli space of semistable cubic fourfolds in terms of a Vinberg-Dynkin diagram. 相似文献
4.
Andreea Munteanu Emilia Petrisor Enrique García-Berro Jordi Jos 《Communications in Nonlinear Science & Numerical Simulation》2003,8(3-4):355
In the present paper, we study the Poincaré map associated to a periodic perturbation, both in space and time, of a linear Hamiltonian system. The dynamical system embodies the essential physics of stellar pulsations and provides a global and qualitative explanation of the chaotic oscillations observed in some stars. We show that this map is an area preserving one with an oscillating rotation number function. The nonmonotonic property of the rotation number function induced by the triplication of the elliptic fixed point is superposed on the nonmonotonic character due to the oscillating perturbation. This superposition leads to the co-manifestation of generic phenomena such as reconnection and meandering, with the nongeneric scenario of creation of vortices. The nonmonotonic property due to the triplication bifurcation is shown to be different from that exhibited by the cubic Hénon map, which can be considered as the prototype of area preserving maps which undergo a triplication followed by the twistless bifurcation. Our study exploits the reversibility property of the initial system, which induces the time-reversal symmetry of the Poincaré map. 相似文献
5.
Poincaré maps have been proved to be a valuable tool in the analysis of non-linear dynamical systems, which usually reduce a continuous phase flow into a two-dimensional discrete map. However, they may be inconvenient for reflecting some characteristics of the system response. In this paper, two novel methods, using the period sampling peak-to-peak value (PSP) diagram and the modified Poincaré map, are presented for characterizing different types of non-linear response. These two methods take advantage of some parameters of the response, such as the peak-to-peak value within an exterior excitation period and the mean value of the displacement. In the PSP diagram method, a two-dimensional graph is plotted by taking the peak-to-peak value as ordinate and the sequential periodically sampling number as abscissa. On the other hand, the modified Poincaré map takes the mean value of the velocity within an exterior excitation period as ordinate and the relevant mean value of the displacement as abscissa. The non-linear responses of a Duffing system, a pendulum with circular motion support and an oscillating circuit are studied by these methods. We also studied the intermittent chaos of the Lorenz system by the PSP diagram method. The PSP diagram is a set of mapping points, which form: a straight line for a one-period response; multi-straight lines for a multi-period response; orderly periodic curves for a quasi-period response; long lines interrupted by transitoriness confusion points for intermittent chaos; and totally out-of-order points for chaos. The figures for the modified Poincaré maps for the period, multi-period, quasi-period responses and chaos are almost identical to those for the Poincaré maps, but the modified maps take more sampling points and can reflect the mean values of the responses. Some numerical results are given based on these methods to show their efficiency in distinguishing different non-linear responses. 相似文献
6.
G. de Vries 《Journal of Nonlinear Science》1998,8(3):281-316
Summary. Bursting oscillations are commonly seen to be the primary mode of electrical behaviour in a variety of nerve and endocrine
cells, and have also been observed in some biochemical and chemical systems. There are many models of bursting. This paper
addresses the issue of being able to predict the type of bursting oscillation that can be produced by a model. A simplified
model capable of exhibiting a wide variety of bursting oscillations is examined. By considering the codimension-2 bifurcations
associated with Hopf, homoclinic, and saddle-node of periodics bifurcations, a bifurcation map in two-dimensional parameter
space is created. Each region on the map is characterized by a qualitatively distinct bifurcation diagram and, hence, represents
one type of bursting oscillation. The map elucidates the relationship between the various types of bursting oscillations.
In addition, the map provides a different and broader view of the current classification scheme of bursting oscillations.
Received October 9, 1996; revised June 16, 1997, and accepted September 26, 1997 相似文献
7.
Yuhua Xu Wuneng Zhou Jian‐an Fang Junhai Ma Yuling Wang 《Mathematical Methods in the Applied Sciences》2011,34(17):2159-2166
A new chaotic system is found by feedback controlling method in this paper. According to the definition of the generalized Lorenz system, the new chaotic system does not belong to generalized Lorenz systems. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map. The particular interest is that this novel system can generate two one‐scroll and one two‐scroll chaotic attractors with the variation of a single parameter. The obtained results show clearly that the system is a new chaotic system and deserves a further detailed investigation. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
A. H. Forrest 《Israel Journal of Mathematics》1997,98(1):101-139
Two ordered Bratteli diagrams can be constructed from an aperiodic substitution minimal dynamical system. One, the proper
diagram, has a single maximal path and a single minimal path and the Vershik map on the path space can be extended homeomorphically
to a map conjugate to the substitution system. The other, the improper diagram, encodes the substitution more naturally but
often has many maximal and minimal paths and no continuous compact dynamics. This paper connects the two diagrams by considering
theirK
0-groups, obtaining the equation
whereQ and ν can be determined from the combinatorial properties of the substitution. This allows several examples of substitution
sequences to be distinguished at the level of strong orbit equivalence.
A final section shows that every dimension group with unit which is a stationary limit of ℤ
n
groups can be represented as aK
0 group of some substitution minimal system. Also every stationary proper minimal ordered Bratteli diagram has a Vershik map
which is either Kakutani equivalent to ad-adic system or is conjugate to a substitution minimal system.
The equation above applies to a much wider class which includes those minimal transformations which can be represented as
a path-sequence dynamical system on a Bratteli diagram with a uniformly bounded number of vertices in each level. 相似文献
9.
We construct a family of triangle-ladder diagrams that can be calculated using the Belokurov-Usyukina loop reduction technique in d=4?2? dimensions. The main idea of the approach we propose is to generalize this loop reduction technique existing in d=4 dimensions. We derive a recurrence relation between the result for an L-loop triangle-ladder diagram of this family and the result for an (L-1)-loop triangleladder diagram of the same family. Because the proposed method combines analytic and dimensional regularizations, we must remove the analytic regularization at the end of the calculation by taking the double uniform limit in which the parameters of the analytic regularization vanish. In the position space, we obtain a diagram in the left-hand side of the recurrence relations in which the rung indices are 1 and all other indices are 1 - ? in this limit. Fourier transforms of diagrams of this type give momentum space diagrams with rung indices 1 - ? and all other indices 1. By a conformal transformation of the dual space image of this momentum space representation, we relate such a family of triangle-ladder momentum diagrams to a family of box-ladder momentum diagrams with rung indices 1 - ? and all other indices 1. Because any diagram from this family is reducible to a one-loop diagram, the proposed generalization of the Belokurov-Usyukina loop reduction technique to a noninteger number of dimensions allows calculating this family of box-ladder diagrams in the momentum space explicitly in terms of Appell’s hypergeometric function F 4 without expanding in powers of the parameter ? in an arbitrary kinematic region in the momentum space. 相似文献
10.
V. A. Timorin 《Functional Analysis and Its Applications》2004,38(1):45-51
Consider a smooth map of a neighborhood of the origin in a real vector space into a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though the origin to the same circles as a Hopf map coming from a representation of a Clifford algebra. We also describe a connection between our result and the Hurwitz–Radon theorem about sums of squares. 相似文献
11.
We consider the dynamics of a harmonically forced oscillator with an asymmetric elastic–perfectly plastic stiffness function. The computed bifurcation diagrams for the oscillator show regions of periodic motion, hysteresis and large regions of chaotic motion. These different regions of dynamical behaviour are plotted in a two-dimensional parameter space consisting of forcing amplitude and forcing frequency. Examples of the chaotic motion encountered are shown using a discontinuity crossing map. Comparisons are made with the symmetric oscillator by computing a typical bifurcation diagram and considering previously published results for the symmetric system. From this we conclude that the asymmetric system is dominated by a large region of chaotic motion whereas in the symmetric oscillator period one motion and coexisting period three motion predominates. 相似文献
12.
Lin Ping Peng 《数学学报(英文版)》2002,18(4):737-754
In this paper, we make a complete study of the unfolding of a quadratic integrable system with a homoclinic loop. Making
a Poincaré transformation and using some new techniques to estimate the number of zeros of Abelian integrals, we obtain the
complete bifurcation diagram and all phase portraits of systems corresponding to different regions in the parameter space.
In particular, we prove that two is the maximal number of limit cycles bifurcation from the system under quadratic non-conservative
perturbations.
Received July 16, 1999, Revised March 15, 2001, Accepted May 25, 2001 相似文献
13.
Ryan Budney 《Advances in Mathematics》2005,191(1):78-113
We initiate the study of classical knots through the homotopy class of the nth evaluation map of the knot, which is the induced map on the compactified n-point configuration space. Sending a knot to its nth evaluation map realizes the space of knots as a subspace of what we call the nth mapping space model for knots. We compute the homotopy types of the first three mapping space models, showing that the third model gives rise to an integer-valued invariant. We realize this invariant in two ways, in terms of collinearities of three or four points on the knot, and give some explicit computations. We show this invariant coincides with the second coefficient of the Conway polynomial, thus giving a new geometric definition of the simplest finite-type invariant. Finally, using this geometric definition, we give some new applications of this invariant relating to quadrisecants in the knot and to complexity of polygonal and polynomial realizations of a knot. 相似文献
14.
We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive
map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we
study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007. 相似文献
15.
证明了赋范空间单位球之间任意保一的1-Lipshcitz算子在假设像空间是严格凸的,或者算子是满的条件下是定义在全空间上的线性等距算子在单位球上的限制.同时,也给出了这个结果的一些应用,以及当两个赋范空间是严格凸时推广了的结果. 相似文献
16.
We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the
Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter
family of universal quadratic Poisson brackets and the Grassmannian is viewed as a Poisson homogeneous space of the general
linear group equipped with an appropriate R-matrix Poisson–Lie structure. We also prove that the Poisson brackets on the Grassmannian
arising in this way are compatible with the natural cluster algebra structure.
相似文献
17.
Zone diagrams are a variation on the classical concept of Voronoi diagrams. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a certain “dominance” map. Asano, Matou?ek, and Tokuyama proved the existence and uniqueness of a zone diagram for point sites in the Euclidean plane, and Reem and Reich showed existence for two arbitrary sites in an arbitrary metric space. We establish existence and uniqueness for n disjoint compact sites in a Euclidean space of arbitrary (finite) dimension, and more generally, in a finite-dimensional normed space with a smooth and rotund norm. The proof is considerably simpler than that of Asano et?al. We also provide an example of non-uniqueness for a norm that is rotund but not smooth. Finally, we prove existence and uniqueness for two point sites in the plane with a smooth (but not necessarily rotund) norm. 相似文献
18.
Rodrigo Treviño 《Israel Journal of Mathematics》2018,225(1):35-70
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of finite area. A criterion of unique ergodicity similar to that of Masur’s for flat surface holds: if there is a subsequence of the renormalizing dynamical system which has a good accumulation point, the translation flow or Bratteli–Vershik transformation is uniquely ergodic. Related questions are explored. 相似文献
19.
We show that when the duality map is norm-to-weak upper semi-continuous at some point of a dual space, the pre-duality map shares this property. We show that if x is a point of very smoothness of a Banach space X, it fails in general to be a point of very smoothness of the bidual X
**. This cannot happen however if the bidual X
** is a Grothendieck space. 相似文献
20.
Andrei Yu. Khrennikov 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):131-139
We perform geometrization of genetics by representing genetic information by points of the 4-adic information space. By a well-known theorem of number theory this space can also be represented as the 2-adic space. The process of DNA reproduction
is described by the action of a 4-adic (or equivalently 2-adic) dynamical system. As we know, the genes contain information
for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as the functioning
of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing
the degenerate structure of the genetic code. We present one of possible solutions of this problem. 相似文献