Report
Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
| العنوان: | Nondegeneracy of heteroclinic orbits for a class of potentials on the plane |
|---|---|
| المؤلفون: | Jendrej, Jacek, Smyrnelis, Panayotis |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 34L05, 34A34, 34C37 |
| الوصف: | 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 $W:\mathbb{R}^m\to\mathbb{R}$, $m\geq 2$, 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 $W:\mathbb{R|^2\to [0,\infty)$ that can be written as $W(z)=|f(z)|^2$, with $f:\mathbb{C} \to \mathbb{C}$ a holomorphic function. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.10804 |
| رقم الانضمام: | edsarx.2109.10804 |
| قاعدة البيانات: | arXiv |
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1 |
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edsarx arXiv edsarx.2109.10804 1022 3 Report report 1021.65399169922 |
| PLink |
https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsarx&AN=edsarx.2109.10804&custid=s6537998&authtype=sso |
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