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1.
The tent map is an ergodic map defined on the unit interval. This paper considers the asymptotic behaviors of the various processes generated by the tent map. We get the uniform versions of law of large numbers for the tent map. An application to Monte Carlo integration is provided. 相似文献
2.
Let a set {Xλ; λ Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace Xλ to define a map gXλ:Xλ→X which has the following property specific to the tent map known in the baker’s transformation. Namely, for any infinite sequence ω0, ω1, ω2, … of Xλ, λ Λ, we can find an initial point x0 ω0 such that gω0(x0)ω1,gω1(gω0(x0))ω2,…. The conditions are successfully applied to a closed cover of a weak self-similar set. 相似文献
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In this paper we study and establish central limit theorem behavior in the skew (generalized) tent map transformation T: Y →Y originally considered by Billings and Bollt [Billings L, Bollt EM. Probability density functions of some skew tent maps. Chaos, Solitons & Fractals 2001; 12: 365–376] and Ito et al. [Ito S, Tanaka S, Nakada H. On unimodal linear transformations and chaos. II. Tokyo J Math 1979; 2: 241–59]. When the measure ν is invariant under T, the transfer operator governing the evolution of densities f under the action of the skew tent map, as well as the unique stationary density, are given explicitly for specific transformation parameters. Then, using this development, we solve the Poisson equation for two specific integrable observables and explicitly calculate the variance σ()2=∫Y2(y)ν(dy). 相似文献
5.
We first introduce tent map base series. The tent map base series is special case of generalized Lüroth series which has the tent map as a base map. Then we study some elementary properties of its error-sum function, and show that the function is continuous. 相似文献
6.
《Nonlinear Analysis: Theory, Methods & Applications》2005,60(1):163-178
The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem and Hopf bifurcation are considered. Appropriate examples are given to ilustrate the bifurcation theorem. 相似文献
7.
《Chaos, solitons, and fractals》2001,12(9):1679-1685
For the area preserving maps, the linearized tangent map determines the stability of the fixed point. When the trace of the tangent map is less than −2, the fixed point is inversion hyperbolic, thus the subsequent points of mapping alternate across the destabilized fixed point. That is to say, the fixed point undergoes periodic doubling bifurcation. While for the trace of the tangent map is larger than +2, the fixed point undergoes the hyperbolic bifurcation without reflection. Here, the processes of the hyperbolic bifurcation without reflection in the standard map have been examined in terms of the higher order symmetry in the momentum inversion. It is shown that the higher order symmetry lines approach asymptotically to the separatrix of the hyperbolic fixed point, and the existing symmetry lines cannot determine the structure of the periodic islands born after the hyperbolic bifurcation without reflection. 相似文献
8.
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
9.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(5):913-927
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot–Julia set of compound logistic map. We generalize the Welstead and Cromer’s periodic scanning technology and using this technology construct a series of Mandelbrot–Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot–Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively. 相似文献
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11.
《随机分析与应用》2013,31(2):375-388
The statistical properties of the Lyapunov exponent of the chaotic generalized skew tent map is studied. Expressions of the mean and the variance of this Lyapunov exponent at each discrete time index are obtained. A sufficient condition for weakly mixing of the chaotic generalized skew tent map is derived, and the asymptotic distribution of its Lyapunov exponent is provided. 相似文献
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A piecewise linear, discontinuous one-dimensional map is analyzed combinatorically. The quasi-periodic dynamics generated by iterations are completely characterized by successive convergents of a continued fraction associated with slopes of the map. 相似文献
14.
一般三角帐篷映射混沌性与两种混沌互不蕴含性 总被引:2,自引:0,他引:2
将三角帐篷映射推广为一般的n-三角帐篷映射,并且借助于一般Bernoulli移位映射,Banks定理与Li-Yorke定理,首先证明:对于任意的正整数n,n-三角帐篷映射既是Devaney混沌的,也是Li-Yorke混沌的.然后,利用所得到的结果,通过实例展示:Devaney混沌与Li-Yorke混沌的互不蕴含性. 相似文献
15.
P. Buser and P. Sarnak showed in 1994 that the maximum, over the
moduli space of Riemann surfaces of genus $s$, of the least
conformal length of a nonseparating loop, is logarithmic in $s$.
We present an application of (polynomially) dense Euclidean packings,
to estimates for an analogous 2-dimensional conformal systolic
invariant of a 4-manifold $X$ with indefinite intersection form. The
estimate turns out to be polynomial, rather than logarithmic, in
$\chi(X)$, if the conjectured surjectivity of the period map is
correct. Such surjectivity is targeted by the current work in gauge
theory. The surjectivity allows one to insert suitable lattices with
metric properties prescribed in advance, into the second de Rham
cohomology group of $X$, as its integer lattice. The idea is to adapt
the well-known Lorentzian construction of the Leech lattice, by
replacing the Leech lattice by the Conway-Thompson unimodular lattices
which define asymptotically dense packings. The final step can be
described, in terms of the successive minima $\lambda_i$ of a lattice,
as deforming a $\lambda_2$-bound into a $\lambda_1$-bound, illustrated
by Figure 1. 相似文献
16.
F. Mañ osas J. Villadelprat 《Proceedings of the American Mathematical Society》2008,136(5):1631-1642
This paper is concerned with the behaviour of the period function of the quadratic reversible centers. In this context the interesting stratum is the family of the so-called Loud's dehomogenized systems, namely In this paper we show that the bifurcation set of the period function of these centers is contained in the rectangle More concretely, we prove that if , then the period function of the center is monotonically increasing.
17.
Thomas J. Bridges 《Journal of Differential Equations》2008,244(7):1629-1674
A fundamental class of solutions of symmetric Hamiltonian systems is relative equilibria. In this paper the nonlinear problem near a degenerate relative equilibrium is considered. The degeneracy creates a saddle-center and attendant homoclinic bifurcation in the reduced system transverse to the group orbit. The surprising result is that the curvature of the pullback of the momentum map to the Lie algebra determines the normal form for the homoclinic bifurcation. There is also an induced directional geometric phase in the homoclinic bifurcation. The backbone of the analysis is the use of singularity theory for smooth mappings between manifolds applied to the pullback of the momentum map. The theory is constructive and generalities are given for symmetric Hamiltonian systems on a vector space of dimension (2n+2) with an n-dimensional abelian symmetry group. Examples for n=1,2,3 are presented to illustrate application of the theory. 相似文献
18.
Supported by the National Science Foundation 相似文献
19.
James Gillespie 《Transactions of the American Mathematical Society》2006,358(7):2855-2874
Let be the category of chain complexes of -modules on a topological space (where is a sheaf of rings on ). We put a Quillen model structure on this category in which the cofibrant objects are built out of flat modules. More precisely, these are the dg-flat complexes. Dually, the fibrant objects will be called dg-cotorsion complexes. We show that this model structure is monoidal, solving the previous problem of not having any monoidal model structure on . As a corollary, we have a general framework for doing homological algebra in the category of -modules. I.e., we have a natural way to define the functors and in .
20.
Computational Management Science - The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the evolution of information modelled by... 相似文献