Abstract
The classical averaging theory is extended to a case where the oscillator admits a homoclinic orbit and the perturbation interacts resonantly with the free oscillations. In the present approach we apply a method of vanishing diffusivity and obtain the weak convergence of the perturbed solutions to the solutions of an appropriately defined averaged system. In the averaged system the concept of probability of trapping appears naturally. The analysis involves an application of basic tools from the Ito calculus followed by a reduction to a priori estimates on a family of parabolic partial differential equations and boundary layer analysis.
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.
