Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8946276 | Journal of Differential Equations | 2018 | 28 Pages |
Abstract
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds. We do not need to know the explicit formulas for the homoclinic orbits prior to the perturbation. We also do not need to compute any integrals along such homoclinics. All needed bounds are established using rigorous computer assisted numerics. Lastly, and most importantly, the method establishes intersections for an explicit range of parameters, and not only for perturbations that are 'small enough', as is the case in the classical Melnikov approach.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Maciej J. CapiÅski, Piotr ZgliczyÅski,