An analytic KAM-Theorem
نویسنده
چکیده
We prove an analytic KAM-theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the theorem presented here is to provide exactly the estimates needed in [1].
منابع مشابه
KAM theory for the Hamiltonian derivative wave equation
We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. 2000AMS subject classification: 37K55, 35L05.
متن کاملKAM Tori for 1D Nonlinear Wave Equations with Periodic Boundary Conditions
with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u = 0. It is proved that for “most” potentials V (x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dim...
متن کاملKAM theory for the reversible derivative wave equation
We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems. 2000AMS subject classification: 37K55, 35L05.
متن کاملKAM Theorem and Quantum Field Theory
We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale by scale. The crucial cancellations of resonances are shown to follow from the Ward identities expressing the translation invariance of the corresponding fie...
متن کاملKAM theory in configuration space and cancellations in the Lindstedt series
The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations between contributio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008