Szczegóły publikacji
Opis bibliograficzny
Beyond the Melnikov method: a computer assisted approach / Maciej J. CAPIŃSKI, Piotr Zgliczyński // Journal of Differential Equations ; ISSN 0022-0396. — 2017 — vol. 262 iss. 1, s. 365–417. — Bibliogr. s. 416–417, Abstr. — Publikacja dostępna online od: 2016-09-28
Autorzy (2)
- AGHCapiński Maciej
- Zgliczyński Piotr
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 102241 |
|---|---|
| Data dodania do BaDAP | 2016-12-21 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jde.2016.09.032 |
| Rok publikacji | 2017 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Differential Equations |
Abstract
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally hyperbolic invariant manifold theorem, which establishes the existence of a NHIM, together with its associated invariant manifolds and bounds on their first and second derivatives. 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. © 2016 Elsevier Inc. All rights reserved.
