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Normal Forms and the Structure of Resonance - Auburn University

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The document discusses the structure of time-dependent resonances in nonlinear time-periodic systems using the method of time-dependent normal forms (TDNF). It employs the Liapunov-Floquet transformation to analyze one and two-degrees-of-freedom systems with quadratic and cubic nonlinearities. The paper presents normal forms, explores higher-order resonances, and demonstrates how to compute resonance sets in parameter space without small parameter restrictions. Examples include a nonlinear Mathieu equation and a double inverted pendulum subjected to periodic forces, illustrating the resonance sets alongside stability boundaries.

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