Concluding Related Topics
The final chapter of this book deals with three topics. In the first part, we study thoroughly the Melnikov function: its computation and structure. We also investigate an inverse problem: the construction of ODEs by prescribed homoclinic solutions. In the second part, as a by product of our investigation, is presented a result of the existence of a transversal homoclinic solution near a transversal homoclinic cycle. We end up with the third part devoted to blue sky catastrophes of periodic solutions.
KeywordsPeriodic Solution Unstable Manifold Homoclinic Orbit Heteroclinic Orbit Exponential Dichotomy
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- 11.A. VANDERBAUWHEDE: Heteroclinic cycles and periodic orbits in reversible systems, in: “Ordinary and Delay Differential Equations”, J. Wiener and J.K. Hale, Eds., Pitman Research Notes in Mathematics Series 272, Pitman, London, 1992, 250–253.Google Scholar