تقرير
Closed geodesics and the first Betti number
| العنوان: | Closed geodesics and the first Betti number |
|---|---|
| المؤلفون: | Contreras, Gonzalo, Mazzucchelli, Marco |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Differential Geometry, Mathematics - Symplectic Geometry, 58E10, 53C22 |
| الوصف: | We prove that, on any closed manifold of dimension at least two with non-trivial first Betti number, a $C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Ma\~n\'e together with the following new theorem of independent interest: the existence of minimal closed geodesics, in the sense of Aubry-Mather theory, implies the existence of a transverse homoclinic, and thus of a horseshoe, for the geodesic flow of a suitable $C^\infty$-close Riemannian metric. Comment: 19 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02995 |
| رقم الأكسشن: | edsarx.2407.02995 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |