On resonances generated by conic diffraction
| Autor: | Jared Wunsch, Luc Hillairet |
|---|---|
| Přispěvatelé: | Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Diffraction
Geodesic Dimension (graph theory) FOS: Physical sciences Lambda 01 natural sciences Mathematics - Spectral Theory Combinatorics Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics 0101 mathematics [MATH]Mathematics [math] Spectral Theory (math.SP) Mathematical Physics ComputingMilieux_MISCELLANEOUS Mathematics Algebra and Number Theory 010102 general mathematics Mathematical Physics (math-ph) Manifold Cone (topology) Conic section 010307 mathematical physics Geometry and Topology Complex plane Analysis of PDEs (math.AP) |
| Zdroj: | Annales de l'Institut Fourier Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2020, 70 (4), pp.1715-1752. ⟨10.5802/aif.3355⟩ |
| ISSN: | 0373-0956 1777-5310 |
| DOI: | 10.5802/aif.3355⟩ |
| Popis: | We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form $$\frac{\Im \lambda}{\log \left |\Re \lambda\right |}= -\nu;$$ here $\nu=(n-1)/2 L_0$ where $n$ is the dimension and $L_0$ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve $$ \frac{\Im \lambda}{\log \left |\Re \lambda\right |}= -\Lambda $$ for a fixed $\Lambda>\nu.$ Comment: Slight correction to main theorem: finitely many different values of the constants $C_\Re$ and $C_\Im$ may be possible if there is more than one maximal diffracted closed orbit. Final version to appear in Ann. Inst. Fourier |
| Databáze: | OpenAIRE |
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