Periodic Solutions of a Newtonian Equation: Stability by the Third Approximation
نویسندگان
چکیده
منابع مشابه
Periodic Solutions of a Newtonian Equation: Stability by the Third Approximation
with z=q+ip, H=| 2T |z| +;1 4T |z| + } } } +;n&1 2nT |z| +r(t, z, z ). The coefficients |, ;1 , ..., ;n&1 are real and r is a T-periodic remainder of order o( |z| ), see [[1], appendice 7]. This is the Birkhoff Normal Form and the numbers ;1 , ..., ;n&1 ,... are the so called twist coefficients. They depend on the derivatives of f (evaluated at % ) up to the order 2n&1 and, when some of them is...
متن کاملL 1 criteria for stability of periodic solutions of a newtonian equation
We develop new criteria for the stability of a periodic solution of a given newtonian equation based on the L-norm of the coefficients of the third order approximation, by proving that the twist coefficient is different form zero.
متن کاملApproximation of periodic solutions for a dissipative hyperbolic equation
This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force f . These approximations are obtained by combining a fixed point algorithm with the Galerkin method. It is known that the energy of the usual discrete models does not decay uniformly with respect to the mesh size. Our aim is to ...
متن کاملLiouville’s equation in post Newtonian approximation I. Static solutions
The post-Newtonian approximation of the general relativistic Liouville’s equation is presented. Two integrals of motion, generalizations of the classical energy and angular momentum, are obtained. Polytropic models are constructed as an application.
متن کاملA conjecture on the stability of the periodic solutions of Ricker's equation with periodic parameters
In this work we propose a conjecture about the stability of the periodic solutions of the Ricker equation with periodic parameters, which goes beyond the existing theory, and for the special case of period-two parameters we analytically show the conjecture is true. For this case we show that the stability region in parameter space obtained from the conjecture is larger than a previously propose...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1996
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0103