Quasi-periodic motions in strongly dissipative forced systems
نویسنده
چکیده
We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing.
منابع مشابه
Construction of quasi-periodic response solutions in forced strongly dissipative systems
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is quasi-periodic solutions which have the same frequency vector as the forcing. This requires dealing with a degenerate implicit function equation: we prove that the l...
متن کاملConvergent series for quasi-periodically forced strongly dissipative systems
We study the ordinary differential equation εẍ+ ẋ+ ε g(x) = εf(ωt), with f and g analytic and f quasi-periodic in t with frequency vector ω ∈ R. We show that if there exists c0 ∈ R such that g(c0) equals the average of f and the first non-zero derivative of g at c0 is of odd order n, then, for ε small enough and under very mild Diophantine conditions on ω, there exists a quasi-periodic solution...
متن کاملDomains of analyticity for response solutions in strongly dissipative forced systems
We study the ordinary differential equation εẍ+ ẋ+ εg(x) = εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c0 ∈ R is such that g(c0) equals the average of f and g(c0) 6= 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c0 with frequency vector ω. We show that such a solution depends analytically on ε in...
متن کاملGlobally and locally attractive solutions for quasi-periodically forced systems
We consider a class of differential equations, ẍ + γẋ + g(x) = f(ωt), with ω ∈ R, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasi-periodicity as the forcing. For g(x) = x, p ∈ N, we show that, when the dissipation coefficient is large enough, there is only one such...
متن کاملSurvey on dissipative KAM theory including quasi-periodic bifurcation theory
Kolmogorov-Arnol’d-Moser Theory classically was mainly developed for conservative systems, establishing persistence results for quasi-periodic invariant tori in nearly integrable systems. In this survey we focus on dissipative systems, where similar results hold. In non-conservative settings often parameters are needed for the persistence of invariant tori. When considering families of such dyn...
متن کامل