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has been cited by the following article:

• TITLE: Reducibility of Periodic Quasi-Periodic Systems

  AUTHORS: Evi Ezekiel, Sangram Redkar

  KEYWORDS: L-P Transformation; Quasi-Periodic System; Reducibility

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.3 No.1, March 17, 2014

  ABSTRACT: In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.