Complete guiding sets for a class of almost-periodic differential equations

A functional differential equation admitting a complete guiding set always has an a priori bounded solution. The introduction of this concept and the idea of reducibility allow the authors to apply a well-known method for the autonomous case to a non-autonomous problem. A previous result of Ortega and Tineo is extended to a non-hyperbolic semilinear functional differential equation with almost-periodic coefficients in its lineal part. The non-hyperbolicity condition is established in terms of the Sacker-Sell spectrum of the associated linear system.     

EXPONENTIAL GROWTH AND OSCILLATION OF NONLINEAR HOMOGENEOUS DIFFERENCEEQUATIONS

1IntroductionConsiderthenonlinearhomogeneousdifferenceequationfwhereashi>0,I--1,''5m,qandrarequotientsofpositiveoddintegers,p20,r=p q,a13'',amarepositiveintegerswithal"<''相似文献   

The nature of the bufferness phenomenon in weakly dissipative systems

We propose a mechanism for accumulating attractors in finite-dimensional weakly dissipative systems. The essence of this mechanism is that if a Hamiltonian or a conservative system with one and a half or more degrees of freedom is perturbed by small additional terms ensuring that it is dissipative, then under certain conditions, the number of its attractors appearing in small neighborhoods of different elliptic equilibriums or cycles of the nonperturbed system can increase without bound as the perturbations tend to zero. We consider meaningful examples from mechanics and radio physics: models of the bouncing ball dynamics, Fermi accelerations, the linear oscillator with impacts, and the self-excited oscillator with a discrete sequence of RLC circuits in the feedback circuit. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 447–466, March, 2006.     

指数型二分性,Melnikov函数和异宿轨道

本文用不同于Ｐａｌｍｅｒ＾［２］的方法，讨论了非自治微分方程存在异宿轨道的条件。得到了已知文献中不同的一个Ｍｅｌｍｉｋｏｖ型的函数。     

Long time behavior of a singular perturbation of the viscous Cahn–Hilliard–Gurtin equation

We consider a singular perturbation of the generalized viscous Cahn–Hilliard equation based on constitutive equations introduced by Gurtin. This equation rules the order parameter ρ, which represents the density of atoms, and it is given on a n‐rectangle (n?3) with periodic boundary conditions. We prove the existence of a family of exponential attractors that is robust with respect to the perturbation parameter ε>0, as ε goes to 0. In a similar spirit, we analyze the stability of the global attractor. If n=1, 2, then we also construct a family of inertial manifolds that is continuous with respect to ε. These results improve and generalize the ones contained in some previous papers. Finally, we establish the convergence of any trajectory to a single equilibrium via a suitable version of the ?ojasiewicz–Simon inequality, provided that the potential is real analytic. Copyright © 2007 John Wiley & Sons, Ltd.     

Transitions torichaos through collisions with hyperbolic orbits

Three models of dissipative dynamical systems are described in which a transition from biperiodic to aperiodic motion proceds via collisions of a hyperbolic orbit with either a torus or a strange attractor.     

Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions

This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced.     

Almost periodic solutions for nonlinear duffing equations

The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation. By combining the theory of exponential dichotomies with Liapunov functions, we obtain an intersting result on the existence of almost periodic solutions. This work is supported by NSF of China, No.19401013     

指数分布尺度参数的区间估计

本文在截尾样本情况下，讨论了指数分布尺度参数的区间估计及其改进