Showing papers on "Asymptotology published in 1983"

Strange attractors and asymptotic measures of discrete-time dissipative systems

Abstract: We investigate asymptotic properties of certain discrete-time dynamical systems in two and three dimensions with solenoidal attractor. It is proved that the asymptotic measures, relevant for the generalized version of the ergodic theorem, all derive from one Haar measure.

Nonlinear time‐dependent anharmonic oscillator: Asymptotic behavior and connected invariants

Abstract: The motion of a particle in a potential decreasing with time as ‖X‖n is considered. Different time and space rescaling are considered in order to obtain the asymptotic solutions. The validity of adiabatic invariants is discussed. The classical critical case corresponds to the obtainment of self‐similar solutions for the quantum problem.

Computations concerning primes and powers of two

Abstract: The problem of representing odd integers as the sum of a prime and a power of two is investigated using numerical computations. The density of representable numbers is calculated up to 231 and the results are extrapolated in order to estimate the asymptotic density. A probabilistic model (suggested by Bombieri) is used to get an independent estimate for the asymptotic density. Either approach suggests 0.434... as a reasonable approximation for the asymptotic density.

On the Leading Term of the Outer Asymptotic Expansion of Van der Pol’s Equation

Abstract: It is proved rigorously that the leading term in the outer asymptotic expansion of the time dependent solution describing relaxation oscillations of the Van der Pol equation is correct. This is accomplished by constructing rigorous estimates of the difference between the exact solution and the outer asymptotic solution as constructed by J. D. Cole. These estimates are both rigorous and numerically computable.

Asymptotic behaviour of Eisenstein integrals

Abstract: Let G be a noncompact connected real semisimple Lie group with finite centre. The asymptotic behaviour of Eisenstein integrals associated with a minimal parabolic subgroup of G has to a large extent been studied by HarishChandra (unpublished work, see [12] for an account, and later in a more general setting in [5-7]). Other references are [9 and 10]. Harish-Chandra's work depends heavily on a detailed study of systems of differential equations satisfied by these integrals. In [1] it is shown that these systems can be transformed into complex differential equations of the regular singular type; the asymptotic behaviour of their solutions is studied by essentially applying the classical Frobenius theory. In this announcement we present some results obtained by using another classical method, namely the representation of solutions of such equations by compact complex contour integrals (for the hypergeometric equation this method goes back to [8]). These integral representations can serve as the starting point for estimation by application of the method of steepest descent. This is closely connected with the use of the method of stationary phase in [2], where the asymptotic behaviour of Eisenstein integrals with respect to the spectral variable is studied. I would like to thank Professor J. J. Duistermaat for suggesting this problem and for the many stimulating discussions we had. Let G = KAN be an Iwasawa decomposition. Let

Momentum from sample paths in stochastic mechanics

Abstract: According to Shucker’s analysis, quantum-mechanical momentum can be read from the asymptotic behaviour of Nelson’s sample paths. Here we use the position-momentum uncertainty product as a measure of the rate of approach to the large time asymptotics.

Asymptotic analysis II : surveys and new trends

Abstract: Dynamical systems driven by small white noise: Asymptotic analysis and applications- to the paper by VF Butuzov and AB Vasil'eva- Singularly perturbed differential equations of parabolic type- Asymptotic methods in mathematical biology- to the paper by AS Bakaj- Integral manifolds and adiabatic invariants of systems in slow evolution- Asymptotic analysis of hamiltonian systems- Homogenization method for the study of composite media- Uniform asymptotic expresions for the fundamental matrix of singularly perturbed linear systems and applications- Slow/fast decoupling for linear boundary value problems- Numerical aspects of singular perturbation problems- The (Driven) Josephson equation: An exercise in asymptotics- Periodic solutions of the autonomous josephson equation- On the interaction of flames and sound- to the research papers- Application of a combined Galerkin-averaging method- Asymptotic expansions for singularly perturbed differential matrix riccati equations with applications to linear - Quadratic optimization problems- Singular perturbations of epidemic models involving a threshold- An asymptotic theory for the free vibrations of an iced two-conductor bundled transmission line- Linear methods in nonlinear problems with a small parameter- Relaxation oscillations including a standard chase on French ducks

Recent trends in asymptotic optimal inference for dependent observations1

Abstract: Summary An overview of some recent developments in the area of asymptotic inference for non-ergodic type stochastic processes is presented. Both local and global formulations of the asymptotic model are given, and non-local optimality results are reviewed. Recent results on conditional inference are briefly discussed. Some open problems and possibilities for new developments are also mentioned.

Second term of the logarithmic asymptotics of path integrals

Abstract: In the survey results are presented related to the construction of asymptotic expansions of Green's function of the Cauchy problem for the heat equation. The basic attention is devoted to the first two terms of the logarithmic asymptotics which are obtained “locally” by probabilistic methods and “globally” by the method of convolution of the sequence of asymptotic solutions over small time.

Asymptotic methods in mathematical biology

Abstract: In this contribution we study asymptotic methods for differential equation models of physiological and ecological phenomena In a survey of the literature special attention is given to the Hopf bifurcation, almost linear oscillations, relaxation oscillations, nonlinear reaction-diffusion and to the change in stability of an ecological system due to periodic forcing

Mathematical properties and asymptotic expansion of the generalized quark statistical function

Abstract: An asymptotic expansion for the generalized quark statistical distributin function in which quarks are introduced into Chao–Yang statistics is derived. Maythematical properties of the function are also examined.