Concluding Related Topics

  • Michal Fečkan
Part of the Nonlinear Physical Science book series (NPS)


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.


Periodic Solution Unstable Manifold Homoclinic Orbit Heteroclinic Orbit Exponential Dichotomy 
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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michal Fečkan
    • 1
  1. 1.Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and InformaticsComenius University Mlynská dolinaBratislavaSlovakia

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