Lagrangian stability of a nonlinear quasi-periodic system
نویسندگان
چکیده
منابع مشابه
Viscous Stability of Quasi-periodic Lagrangian Tori
We consider a smooth Tonelli Lagrangian L : TTn → R and its viscosity solutions u(x, P ) characterized by the cell equation H(x, P + Dxu(x, P )) = H(P ), where H : T ∗Tn → R is the Hamiltonian associated with L. We will show that if P0 corresponds to a quasi-periodic Lagrangian invariant torus, then Dxu(x, P ) is Hölder continuous in P at P0 with Hölder exponent arbitrarily close to 1, and if b...
متن کاملThe Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems
and Applied Analysis 3 2. Main Result We first give some definitions 12 . Definition 1. A function f : R → R is called real analytic quasi-periodic with frequencies μ1, . . . , μm if it can be represented as a Fourier series of the type
متن کاملQuasi - periodic Nonlinear Photonic Crystal
2 3 The second issue of SCE-Science opens up the aperture to a wider glance at the diverse and innovative research conducted at SCE-Sha-moon College of engineering. The articles brought here present just a small portion of the bustling activity of creation, cooperation, and study felt throughout our college. In this issue are represented some of our senior researchers as well as some of our lat...
متن کاملQuasi-periodic stability of normally resonant tori
We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorovlike variation of the internal frequencies and simultaneously versality of the Floquet matrix ...
متن کاملPeriodic, quasi-periodic, and random quadratic nonlinear photonic crystals
Quadratic nonlinear photonic crystals are materials in which the second order susceptibility is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirement...
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 Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.01.003