The Ambrosetti-Prodi periodic problem: Different routes to complex dynamics

2017/09/17 by Elisa Sovrano, Sovrano, Elisa, Fabio Zanolin +1
Mathematics · Physics and Astronomy · #34C25 #34C28 #37G20 #54H20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1709.05677

openalex publication_date 2017/09/17 · openalex created_date 2017/09/25 · openalex updated_date 2026/07/28

Abstract

We consider a second order nonlinear ordinary differential equation of the form u'' + f(u) = p(t) where the forcing term p(t) is a T-periodic function and the nonlinearity f(u) satisfies the properties of Ambrosetti-Prodi problems. We discuss the existence of infinitely many periodic solutions as well as the presence of complex dynamics under different conditions on p(t) and by using different kinds of approaches. On the one hand, we exploit the Melnikov's method and, on the other hand, the concept of "topological horseshoe".

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