Abstract
This paper presents a new unified theory of orbits homoclinic to resonance bands in a class of near-integrable dissipative systems. It describes three sets of conditions, each of which implies the existence of homoclinic or heteroclinic orbits that connect equilibria or periodic orbits in a resonance band. These homoclinic and heteroclinic orbits are born under a given small dissipative perturbation out of a family of heteroclinic orbits that connect pairs of points on a circle of equilibria in the phase space of the nearby integrable system. The result is a constructive method that may be used to ascertain the existence of orbits homoclinic to objects in a resonance band, as well as to determine their precise shape, asymptotic behavior, and bifurcations in a given example. The method is a combination of the Melnikov method and geometric singular perturbation theory for ordinary differential equations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
