On the existence of connecting orbits for critical values of the energy

2017/01/25 by Giorgio Fusco, Fusco, Giorgio, Giovanni F. Gronchi +3
Physics and Astronomy · Mathematics · Engineering · #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1701.07514

Abstract

We consider an open connected set Ω and a smooth potential U which is positive in Ω and vanishes on ∂Ω. We study the existence of orbits of the mechanical system u=U_x(u), that connect different components of ∂Ω and lie on the zero level of the energy. We allow that ∂Ω contains a finite number of critical points of U. The case of symmetric potential is also considered.

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