Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
| Autor: | Panayotis Smyrnelis, Jacek Jendrej |
|---|---|
| Přispěvatelé: | Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Basque Center for Applied Mathematics (BCAM), Basque Center for Applied Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Class (set theory) Mathematics::Dynamical Systems Plane (geometry) Applied Mathematics 010102 general mathematics Scalar (mathematics) Holomorphic function Perturbation (astronomy) 01 natural sciences 010101 applied mathematics Nonlinear system Mathematics - Analysis of PDEs 34L05 34A34 34C37 FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Applied Mathematics Letters Applied Mathematics Letters, Elsevier, In press Applied Mathematics Letters, Elsevier, In press, 124, ⟨10.1016/j.aml.2021.107681⟩ |
| ISSN: | 0893-9659 |
| DOI: | 10.1016/j.aml.2021.107681⟩ |
| Popis: | In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the vector case this assumption is generic, in the sense that for any potential W : R m → R , m ≥ 2 , there exists an arbitrary small perturbation of W , such that for the new potential minimal heteroclinic orbits are nondegenerate. However, to the best of our knowledge, nontrivial explicit examples of such potentials are not available. In this paper, we prove the nondegeneracy of heteroclinic orbits for potentials W : R 2 → [ 0 , ∞ ) that can be written as W ( z ) = | f ( z ) | 2 , with f : ℂ → ℂ a holomorphic function. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect