Bounding Solutions of a Forced Oscillator.

Authors :: Meyer, Kenneth R.
Schmidt, Dieter S.
Source :: Journal of Dynamics & Differential Equations. Sep2019, Vol. 31 Issue 3, p1129-1139. 11p.
Publication Year :: 2019
Abstract: We give an alternate proof of a theorem in Wang and You (Z Angew Math Phys 47: 943–952, 1996) which shows that all solutions are bounded for a periodically forced nonlinear oscillator. Our proof relies on constructing an analytic change of variables by a convergent Lie series transformation to simplify the system so that the period map has large invariant curves by Moser's theorem. [ABSTRACT FROM AUTHOR]