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1.
Letf a a∈A be a C2 one-parameter family of non-flat unimodal maps of an interval into itself anda* a parameter value such that
- fa* satisfies the Misiurewicz Condition,
- fa* satisfies a backward Collet-Eckmann-like condition,
- the partial derivatives with respect tox anda of f a n (x), respectively at the critical value and ata*, are comparable for largen.
2.
We establish that the reducibility exponent (Differentsial’nye Uravneniya, 2007, vol. 43, no. 2, pp. 191–202) of each linear system , with piecewise continuous bounded coefficient matrix A does not belong to the set of values of σ for which the perturbed system (1A+Q) with an arbitrary piecewise continuous perturbation Q satisfying the condition \(\overline {\lim } _{t \to + \infty } t^{ - 1} \ln \left\| {Q(t)} \right\| \leqslant - \sigma \) is reducible to the original system (1 A ) by some Lyapunov transformation.
相似文献
$$\dot x = A(t)x, x \in \mathbb{R}^n , t \geqslant 0$$
3.
V. I. Zalygina 《Differential Equations》2014,50(10):1314-1321
We show that any linear homogeneous differential system can be reduced by some linear piecewise differentiable transformation whose matrix, together with its inverse, is bounded on the half-line to a system with piecewise constant coefficients of the same growth order, and any system with a uniformly small perturbation can be reduced by this linear transformation to the same system with a piecewise constant perturbation of the same smallness. 相似文献
4.
E. A. Barabanov 《Differential Equations》2009,45(8):1087-1104
We consider families of linear differential systems continuously depending on a real parameter with continuous (or piecewise
continuous) coefficients on the half-line. The improperness set of such a family is defined as the set of all parameter values
for which the corresponding systems in the family are Lyapunov improper. We show that a subset of the real axis is the improperness
set of some family if and only if it is a G
δσ
-set. The result remains valid for families in which the matrices of the systems are bounded on the half-line. Almost the
same result holds for families in which the parameter occurs only as a factor multiplying the system matrix: their improperness
sets are the G
δσ
-sets not containing zero. For families of the last kind with bounded coefficient matrix, we show that their improperness
set is an arbitrary open subset of the real line. 相似文献
5.
This paper addresses the problem of approximately computing the Lyapunov exponent of stochastic max-plus linear systems. Our approach allows for an efficient simulation of bounds for the Lyapunov exponent. We provide sufficient conditions for the convergence of the bounds. In particular, a perfect sampling scheme for the Lyapunov exponent is established. We illustrate the effectiveness of our bounds with an application to (real-life) railway systems. 相似文献
6.
Christophe Abraham Grard Biau Benoît Cadre 《Journal of Mathematical Analysis and Applications》2004,290(2):395-404
Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. For a large class of transformations of the interval, we prove that positiveness of the Lyapunov exponent implies the sensitivity property. We also provide bounds for the sensitivity constant. 相似文献
7.
8.
K. E. Shiryaev 《Differential Equations》2014,50(10):1418-1423
We show that the generalized logarithmic exponent of an n-dimensional homogeneous linear differential system with continuous bounded coefficients on the half-line treated as a function of its right-hand side on the set of all such systems equipped with the topology of uniform convergence belongs exactly to the second Baire class if n ≥ 2 and to the zero Baire class if n = 1. 相似文献
9.
10.
V. V. Mitsenko 《Differential Equations》2014,50(10):1336-1341
We show that the set of values of the upper wanderability exponent of nonzero solutions of linear two-dimensional triangular homogeneous differential systems with coefficients bounded in absolute value on the half-line by a number M is the interval [0,M]. 相似文献
11.
Andrzej Stefanski 《Chaos, solitons, and fractals》2000,11(15):2443-2451
The method of estimation of the largest Lyapunov exponent for mechanical systems with impacts using the properties of synchronization phenomenon is demonstrated. The presented method is based on the coupling of two identical dynamical systems and is tested on the classical Duffing oscillator with impacts. 相似文献
12.
N. K. Krivulin 《Vestnik St. Petersburg University: Mathematics》2009,42(2):95-105
A stochastic dynamic system of second order is considered. The system evolution is described by a dynamic equation with a stochastic transition matrix, which is linear in the idempotent algebra with operations of maximum and addition. It is assumed that some entries of the matrix are zero constants and all other entries are mutually independent and exponentially distributed. The problem considered is the computation of the Lyapunov exponent, which is defined as the average asymptotic rate of growth of the state vector of the system. The known results related to this problem are limited to systems whose matrices have zero off-diagonal entries. In the cases of matrices with a zero row, zero diagonal entries, or only one zero entry, the Lyapunov exponent is calculated using an approach which is based on constructing and analyzing a certain sequence of one-dimensional distribution functions. The value of the Lyapunov exponent is calculated as the average value of a random variable determined by the limiting distribution of this sequence. 相似文献
13.
14.
A. N. Vetokhin 《Differential Equations》2013,49(4):399-405
We establish the sharp Baire class of the Lyapunov exponents on the space of Lyapunov regular linear systems with continuous bounded coefficients equipped with the topology of uniform or compact convergence of the coefficients on the half-line. 相似文献
15.
A. S. Voidelevich 《Differential Equations》2014,50(10):1300-1313
For a linear differential system, we obtain formulas for the computation of the exact boundaries of upper mobility for Lyapunov exponents under exponentially decaying perturbations of its coefficient matrix on the basis of the Cauchy matrix. 相似文献
16.
Summary The author proves the consistency of a nearest neighbor estimator of the Lyapunov exponent for a general class of one-dimensional
ergodic dynamical systems. The author shows that this estimator has good practical properties on a set of simulations. 相似文献
17.
18.
N. E. Barabanov 《Siberian Mathematical Journal》1988,29(4):521-530
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 4, pp. 12–22, July–August, 1988. 相似文献
19.
T. M. Aldibekov 《Russian Mathematics (Iz VUZ)》2010,54(5):1-5
We study the generalized Lyapunov exponents, i.e., the Lyapunov exponents in a more general scale, and apply them for studying
the asymptotics of the growth of solutions to differential systems. We obtain necessary and sufficient conditions for the
upper semicontinuity of the senior generalized Lyapunov exponents in a class of systems of differential equations. 相似文献