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タイトル: | The Stokes geometry of the quantum Henon map in the horseshoe regime : Dedicated to Professor Takashi Aoki on the occasion of his 60th birthday (Exponential Analysis of Differential Equations and Related Topics) |
著者: | Shudo, Akira |
著者名の別形: | シュドウ, アキラ |
キーワード: | 34E20 37D20 Stokes geometry saddle point method Quantum Henon map Smale's horseshoe |
発行日: | Nov-2014 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B52 |
開始ページ: | 263 |
終了ページ: | 282 |
抄録: | The Stokes geometry for the propagator of the quantum Hénon map is studied in the light of recent developments of the exact WKB analysis, especially in the case where the Hénon map satisfies the horseshoe condition. Our analysis reveals that the birth and death of the WKB solutions caused by the Stokes phenomenon do not occur in a local but entirely global manner, reflecting topological nature encoded in the Stokes geometry. We derive an explicit general formula to enumerate the number of WKB solutions in the asymptotic region and obtain its growth rate, which is shown to be less than the topological entropy of the corresponding classical dynamics. |
記述: | "Exponential Analysis of Differential Equations and Related Topics". October 15~18, 2013. edited by Yoshitsugu Takei. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2014 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/232923 |
出現コレクション: | B52 Exponential Analysis of Differential Equations and Related Topics |
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